Prove that matrix addition is commutative for 2 × 2 matrices.
Answers
We have shown that matrix addition is commutative for 2 × 2 matrices, as the sum of any two 2 × 2 matrices is the same regardless of the order of addition.
To prove that matrix addition is commutative for 2 × 2 matrices, we need to show that for any two 2 × 2 matrices A and B, the following equality holds:
A + B = B + A
Let's consider two arbitrary 2 × 2 matrices:
A = [a₁₁ a₁₂]
[a₂₁ a₂₂]
B = [b₁₁ b₁₂]
[b₂₁ b₂₂]
To prove the commutativity of matrix addition, we need to show that the sum of matrices A and B is equal to the sum of matrices B and A.
The sum of A and B is given by:
A + B = [a₁₁ + b₁₁ a₁₂ + b₁₂]
[a₂₁ + b₂₁ a₂₂ + b₂₂]
Similarly, the sum of B and A is given by:
B + A = [b₁₁ + a₁₁ b₁₂ + a₁₂]
[b₂₁ + a₂₁ b₂₂ + a₂₂]
Now, let's compare the elements of the matrices A + B and B + A:
(a₁₁ + b₁₁) = (b₁₁ + a₁₁)
(a₁₂ + b₁₂) = (b₁₂ + a₁₂)
(a₂₁ + b₂₁) = (b₂₁ + a₂₁)
(a₂₂ + b₂₂) = (b₂₂ + a₂₂)
We can observe that each element in A + B is equal to the corresponding element in B + A. Since this holds true for all elements, we can conclude that A + B is indeed equal to B + A.
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Related Questions
Circle M has the central angle LAMB with a measure of 63º. Which of the following statements does not represent the
circle M?
O AB is a minor arc
O mAB=63
The center of the circle is point M.
O AB is a major arc
Answers
Answer:
O AB is a major arc
Step-by-step explanation:
Circle M has the central angle LAMB with a measure of 63º
Which of the following statements does not represent the circle M?
----------------
O AB is a minor arc
yes, it is 63º, less than halfO mAB=63 º
yesO The center of the circle is point M.
yesO AB is a major arc
no, it is not more than half11/12 = 4h solve for h
(With explanations please.)
Answers
Answer:
h = 11/48
Step-by-step explanation:
We need to isolate the variable h to solve for the value of h
11/12 = 4h
If we divide both sides by 4, we can get the value of h. When we divide, we need to multiply by the reciprocal of 4 with 11/12. The reciprocal of 4 is 1/4.
11/12(1/4) = h
h = 11/48
The ratio of 3 to 4 and the ratio of 4 to 3___ the same number? A are not b are.
Answers
Answer: Option B
Step-by-step explanation:
By definition, the ratio is a comparison between two different things. It can be written in:
Odd notation
\(a:b\)
Fractional notation
\(\frac{a}{b}\)
Or in words:
\(a\) \(to\) \(b\)
Given the ratio 3 to 4 and the ratio of 4 to 3, you can rewrite them the fractional form:
\(\frac{3}{4}\)
\(\frac{4}{3}\)
To know if these ratios are the same number, divide the numerator by the denominator of each one of them:
\(\frac{3}{4}=0.75\)
\(\frac{4}{3} =1.33\)
Therefore, the ratio of 3 to 4 and the ratio of 4 to 3 ARE NOT the same number.
what is the list after the second outer loop iteration?[6,9,8,1,7],[],,,
Answers
After the second outer loop iteration, the list is [6,1,7,8,9].
To determine the list after the second outer loop iteration, let's assume we're working with a simple bubble sort algorithm. Here are the steps:
1. First outer loop iteration:
- Compare 6 and 9; no swap.
- Compare 9 and 8; swap to get [6,8,9,1,7].
- Compare 9 and 1; swap to get [6,8,1,9,7].
- Compare 9 and 7; swap to get [6,8,1,7,9].
2. Second outer loop iteration:
- Compare 6 and 8; no swap.
- Compare 8 and 1; swap to get [6,1,8,7,9].
- Compare 8 and 7; swap to get [6,1,7,8,9].
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Match the missing parts of the triangle with their correct length or measure.
HINT: The ONLY right triangles we are given in this problem are ADB and BDC. Triangle ABC is NOT necessarily a right triangle.
Given:
DB=24
AD=32
AC=42
DC=10
BC=26
AB=40
Measure
Measure of
Find:
Measure
Measure
Measure
Measure
Measure
Answers
The length of DB, AD and AC are 24 m, 32 m, 42 m respectively. The measurement of ∠C = 67.38°.
What is a right angle triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Given that, in △BCD
BD = 24 m
DC = 10 m
BC = 26 m
△BCD is a right angle triangle.
The trigonometry ratio of sine is ratio of height to hypothenuse.
With respect to C, the height of △BCD is 24m and hypothenuse is 26m.
sin C = height/hypothenuse
sin C = 24/26
C = 67.38°
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Which statement does not describe the tangent function?
A. The cycle repeats every 2pi radians.
B. Its range includes all real numbers.
C. Its reciprocal function is cotangent.
D. The graph has asymptotes, including one at x =pi/2
radians.
Answers
Answer:the cycle repeats every 2pi radians
Step-by-step explanation:
Answer:
The statement which does not describe the tangent function is A. The cycle repeats every 2pi radians.
Step-by-step explanation:
Tangent functionThe tangent function is the ratio of the length of the opposite side to that of the adjacent side. It is also described as the ratio of sine and cos .
If we analyses the tan function graph we will happened to find that it repeats itself after every π radian .
So, its cycle cannot repeat every 2pi radians.
Therefore, The statement which says that The cycle repeats every 2pi radians does not describe the tangent function.
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How to write 8,99,999 in international system. I want this number but in words of international system
Answers
8,99,999 in international system:-
899,999= Eight hundred ninety-nine thousand nine hundred ninety-nine
Summarize the three conditions that must be checked before carrying out significance tests.
Answers
We introduced three conditions that should be met before we construct a confidence interval for an unknown population proportion: Random, Normal, and Independent.
What is random, normal and independent conditions?There are three crucial requirements that must be met in order to establish a confidence interval. These are Independent, Random, and Normal.
Any survey is carried out objectively.
It is required to assure randomness. An independent choice is equally likely to be made in a random sample. Similar to how the confidence interval is built, normal is used to confirm which phenomena are being employed or to correct the approach if necessary. In a similar vein, independent is crucial because it contains the facts to be analyzed. For the purpose of calculating the standard deviation, independent is used.
Therefore, it's crucial to consider the Random, Normal, and Independent criteria while building a confidence interval.
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I need help with 18 and 22 thx
Answers
The proportional relationships for these problems are given as follows:
18. y = 0.5x, with constant k = 0.5.
22. y = -0.4x, with constant k = -0.4.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In item 18, we have that when x = 2, y = 1, hence the constant is:
k = y/x = 1/2 = 0.5.
Hence the equation is:
y = 0.5x.
In item 22, we have that when x = -5, y = 2, hence the constant is:
k = y/x = -2/5 = -0.4.
Hence the equation is:
y = -0.4x.
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Laura wants to know the volume of her gold ring in cubic centimeters. She gets a rectangular glass with a base 7\text{ cm}7 cm7, start text, space, c, m, end text by 4.5\text{ cm}4.5 cm4, point, 5, start text, space, c, m, end text and fills the glass 8.8\text{ cm}8.8 cm8, point, 8, start text, space, c, m, end text high with water. Laura drops her gold ring in the glass and measures the new height of the water to be 9.2\text{ cm}9.2 cm9, point, 2, start text, space, c, m, end text. What is the volume of Laura's ring in cubic centimeters
Answers
The volume of her gold ring in cubic centimeters will be 12.6 cubic centimeters.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H.
a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases.
Then the volume of the prism is given as
V = L x W x H
She gets a rectangular glass with a base of 7 cm by 4.5 cm and fills the glass 8.8 cm high with water.
Laura drops her gold ring into the glass and measures the new height of the water to be 9.2 cm.
Then the volume of her gold ring in cubic centimeters will be
V = 7 × 4.5 ×(9.2 - 8.8)
V = 7 × 4.5 × 0.4
V = 12.6 cubic centimeters
The volume of her gold ring in cubic centimeters will be 12.6 cubic centimeters.
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Figure 222 is a scaled copy of Figure 111.
PLEASE HELP
Identify the side in Figure 222 that corresponds to side \overline{CD}
CD
start overline, C, D, end overline in Figure 111.
Choose 1 answer:
Choose 1 answer:
Answers
What is the equation of the line that passes through the point (-6,3) and has a
slope of -1/6?
Answers
Answer:
y = -1/6x + 2
Step-by-step explanation:
Put it in point-slope form:
y - 3 = -1/6(x + 6)
y -3 = -1/6x - 1
y = -1/6x + 2
16 is what percent of 96?
Answers
Answer:
15.36%
Step-by-step explanation:
There are three different cubes such that the first cube is 64 times the volume of the second, and the volume of the second cube is 27 times less than the volume of the third. Which among the following is the ratio of the side of the first cube to third cube?
Answers
Answer:
4/3
Step-by-step explanation:
If the ratio between the volumes of the first and the second cube is 64, the ratio between the sides is the cubic root of the ratio between the volumes, so:
\(V1 / V2 = 64\)
\(s1 / s2 = \sqrt[3]{64} = 4\)
Doing the same for the second and third cubes, we have:
\(V2 / V3 = 1/27\)
\(s2/ s3 = \sqrt[3]{1/27} = 1/3\)
So the ratio of the first cube side and the third cube side is:
\(s1 / s3 = (s1/s2) * (s2/s3) = 4 * (1/3) = 4/3\)
Find the total cost: $20 meal; 7% sales tax; 20% tip (do the tip before tax)
Answers
Answer:
$25.40
Step-by-step explanation:
1) Calculating tip
$20 x (20/100) = $4
2) Calculating sales tax
$20 x (7/100) = $1.4
3) Calculating Total cost of meal
$20 + $4 + $1.4 = $25.4
if the vertex of a parabola is (5,-10) what is the axis of symmetry?
Answers
The axis of symmetry of a parabola with vertex (5, -10) is x = 5, which is a vertical line passing through the vertex.
The axis of symmetry of a parabola is a vertical line that passes through its vertex and divides the parabola into two mirror-image halves. In this case, the vertex of the parabola is given as (5, -10), which means the vertex lies on a horizontal line passing through the axis of symmetry.
The equation of the axis of symmetry can be written as x = h, where (h, k) is the vertex of the parabola.
As from the given points h corresponds to value '5'. Therefore, the axis of symmetry for this parabola is x = 5, which is a vertical line passing through the point (5, -10).
To visualize this, you can imagine folding the parabola along its axis of symmetry. The left and right halves of the parabola will overlap perfectly, creating a symmetrical shape.
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Help me out with this question!! 50 points
Answers
C
The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C
The correct answer is D) The first inequality should be s + h ≤ 1800.
The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.
The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.
Logan is doing a handstand dive from a 12 meter platform. The equation that models the path of her dive is given by LaTeX: h=-4.9t^2+12h = − 4.9 t 2 + 12, where t is seconds. After how many seconds will Logan hit the water?
Answers
Answer:
Time, t = 2.44 seconds
Step-by-step explanation:
Logan is doing a handstand dive from a 12 meter platform. The equation that models the path of her dive is given by :
\(h=-4.9t^2+12t\)
It is required to find the time after which Logan will hit the ground. At this point, h = 0
\(-4.9t^2+12t=0\\\\t(-4.9t+12)=0\\\\t=\dfrac{12}{4.9}\\\\t=2.44\ s\)
So, after 2.44 seconds it will hit the water.
The variance of the return on a portfolio with many securities is _______ dependent on the covariances between the individual securities than on the variances of the individual securities.
Answers
The variance of the return on a portfolio with many securities is more dependent on the covariances between the individual securities than on the variances of the individual securities.
The variance of a portfolio measures the variability or dispersion of the portfolio's returns. When a portfolio consists of multiple securities, the overall variance is influenced by the interrelationships among the returns of those individual securities.
The covariance between individual securities in a portfolio has a significant impact on the portfolio's variance.
The diversification benefits arise from the fact that covariances tend to offset each other, potentially leading to a lower overall portfolio variance compared to the sum of individual variances.
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Graph the solution to this inequality on the number line. −1/2x+3/4>−2/3
Answers
Answer:
Step-by-step explanation:
Answer:
To graph the solution to the inequality -1/2x+3/4>-2/3 on the number line, we need to solve for x first.
-1/2x+3/4>-2/3
-1/2x>-2/3-3/4
-1/2x>-17/12
x<17/12*2
x<17/6
The solution is x<17/6. To graph this on the number line, we draw an open circle at 17/6 and shade everything to the left of it since x is less than 17/6.
y is 5 less than the square of the sum of p and q.
Write down a formula for y in terms of p and q.
Answers
Answer:
y = (p+q)² - 5
Step-by-step explanation:
Use the wording to do this:
y = (p+q)² - 5
I know that this is a lot but I’m in desperate need of help!! Thank you
Answers
Answer:
1) 12 x 6 x 3 = 216
2)10 x 10 x 4 = 400
3) 11 x 8 x 8 = 704
4) 4 x 1 x 3 / 2
i gave you the answers for the first 4 ,
i think you can do the rest
Step-by-step explanation:
volume = base x length x width
El ruedo de la plaza de toros "Las Ventas", de
Madrid, España mide 61. 5 metros de diámetro,
mientras que el de la Plaza "México", tiene una
circunferencia de 135. 02 metros. ¿Cuál de los dos
ruedos es más grande?
Answers
Answer:
mention any one contribution of maiti nepal
what type of triangle is this?
Answers
Just wanna thank everyone on this app for helping me pass my sophomore year bc without y’all i would be in deep sh*t everyone have a great summer and live it up
Answers
Answer:
this app is good
Step-by-step explanation:
yah
what is represented by the distance between two vertical white gridlines on this graph? what is represented by the distance between two vertical white gridlines on this graph? a population increase of 20 million a population increase of 2 billion a time span of 20 years a time span of 50 years
Answers
The distance between two vertical white gridlines on a graph typically represents a specific interval or scale.
Based on the options you provided, the correct answer would depend on the context of the graph.
If the graph is displaying population data over time, the distance between two vertical white gridlines could either represent:
- A time span of 20 years
- A time span of 50 years
If the graph is displaying population increase directly, the distance could represent:
- A population increase of 20 million
- A population increase of 2 billion
To determine the correct answer, please examine the labels and context of the graph you are analyzing.
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I don’t know if this is correct !!!!!!! Please answer correctly !!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!
Answers
HELP IM BEING TIMEDDDDDDDDDDDDDDDDDDDDDD
Answers
Answer:11
Step-by-step explanation:
Answer:19
Step-by-step explanation:15+4=19
19-15=4
the degenerative disease osteoarthritis most frequently affects weight-bearing joints such as the knee. an article presented the following summary data on stance duration (ms) for samples of both older and younger adults. age n sample mean sample sd older 28 801 117 younger 16 780 72 assume that both stance duration distributions are normal. a) calculate and interpret a 99% confidence interval (ci) for true average stance duration among elderly individuals. b) carry out a test of hypotheses to decide whether true average stance duration is larger among elderly individuals than among younger individuals. c) construct a 95% ci for the difference in means and compare results to part(b).
Answers
We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.
To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)
Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic
a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.
Given:
Older adults: n = 28, sample mean = 801, sample standard deviation = 117
Using the formula for a confidence interval for the mean, we have:
Margin of error = t * (sample standard deviation / √n)
Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.
Calculating the margin of error:
Margin of error = 2.576 * (117 / √28) ≈ 56.44
The confidence interval is then calculated as:
Confidence interval = (sample mean - margin of error, sample mean + margin of error)
Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)
b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.
The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.
The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.
. With the given data, perform the t-test and obtain the p-value.
c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.
Given:
Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117
Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72
Calculating the standard error of the difference in means:
Standard error = √((s1^2 / n1) + (s2^2 / n2))
Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89
Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.
Calculating the margin of error:
Margin of error = t * standard error
Margin of error = 2.048 * 33.89 ≈ 69.29
The confidence interval is then calculated as:
Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)
Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)
Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.
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Explain why the set of natural numbers {1,2,3,4,...} and the set of even numbers {2, 4, 6, 8, . . .} of positive even numbers
Answers
The set of natural numbers {1,2,3,4,...} and the set of positive even numbers {2, 4, 6, 8, . . .} are different because natural numbers include all positive integers, while even numbers only include those that are divisible by 2 with no remainder.
About the setsTwo important sets of numbers are natural numbers and even numbers. The set of natural numbers consists of numbers that are not negative, beginning with 1 and continuing indefinitely with 2, 3, 4, and so on.
The set of even numbers, on the other hand, consists of numbers that are divisible by 2, beginning with 2, 4, 6, and so on.
Positive integers refer to natural numbers. Any integer greater than zero is a positive integer.
Zero is not a positive integer. Hence, the set of natural numbers consists of {1,2,3,4,…}
On the other hand, the set of even numbers consists of {2, 4, 6, 8, . . .}.
Therefore, {1,2,3,4,…} and {2, 4, 6, 8, . . .} are two different sets of numbers where one set is composed of positive integers (natural numbers) and the other is composed of positive even numbers.
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