what is the determinant of an elementary row replacement matrix?an elementary nxn row replacement matrix is the same as the nxn identity matrix with of the replaced with some number k. this means it is and so its determinant is the of its diagonal entries. thus, the determinant of an elementary row replacement matrix is
Answers
The determinant of an elementary row replacement matrix is the product of its diagonal entries.
So if we have a matrix E with diagonal entries d1, d2, ..., dn, the determinant of E is:
determinant(E) = d1×d2×...×dn
What is an elementary row replacement matrix?An elementary row replacement matrix is a matrix that is formed by performing an operation on an identity matrix, which is nxn. Row replacement is a basic operation in linear algebra in which a row is multiplied by a scalar and then added to another row. These basic row operations are called elementary row operations.
Let's take an example to understand this more clearly. Consider the matrix given below:
[1, 3, 1][1, 0, 0][2, 2, 2]
We want to replace the third row with the first row multiplied by 2 and subtracted from the third row, the matrix would be:
[1, 3, 1][1, 0, 0][0, -4, 0]
The matrix resulting from this operation is an elementary row replacement matrix. We can see that the matrix has the form of an identity matrix with one nonzero entry. Since the determinant of an identity matrix is 1, we can also say that the determinant of an elementary row replacement matrix is the same as the determinant of the matrix resulting from the operation.To calculate the determinant of an elementary row replacement matrix, we use the formula for the determinant of a matrix. The determinant of a matrix is the sum of the products of the elements in each row and column. The formula for the determinant of an nxn matrix is:
|A| = a11 A11 + a12 A12 + ... + a1n An1
where Aij is the cofactor of the element aij. The determinant of an elementary row replacement matrix is the product of its diagonal entries.
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Related Questions
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the vectors u = <-1, -3>, V = <5,-8>, W = <5, -2>, and z = <3, 1>.
Based on the components of vectors U, V, W, and Z match each vector subtraction with the magnitude of the resulting vector.
Answers
Answer:
1. ║u-z║= 5.66
2.║v-w║=6.0
3. ║w-u║=6.08
4.║v-u║=7.81
Step-by-step explanation:
The vectors are given as;
u = <-1, -3>, v = <5,-8>, w = <5, -2>, and z = <3, 1>.
To find the magnitude of the vectors;
1. ║u-z║
<-1 - 3> = <-4 and < -3 - 1> = <-4
║<-4,-4> ║= √{ -4²+-4²} = √32 = 5.66
2.║v-w║
<5,-8> - <5,-2>
<5-5> , <-8--2>
<0,-6>
║<0,-6>║= √{0²+ -6²} = √36 = 6
3. ║w-u║
<5,-2> - <-1,-3>
<5--1> , <-2--3>
<6,1>
║6,1║= √{6²+1²} = √36+1 = √37 = 6.08
4.║v-u║
<5,-8> - <-1,-3>
<5--1> , <-8--3>
< 6 , -5 >
║6,-5║= √{6²+-5²} = √36+25 =√61 = 7.81
Answer:
Step-by-step explanation:
2. find the general solution of the system of differential equations d dt x = 9 3
Answers
The general solution to the system of differential equations dx/dt = 9, dy/dt = 3y is:
\(x(t) = 9t + C1\\y(t) = Ce^{(3t)} or y(t) = -Ce^{(3t)\)
To solve this system, we can start by integrating the first equation with respect to t:
x(t) = 9t + C1
where C1 is a constant of integration.
Next, we can solve the second equation by separation of variables:
1/y dy = 3 dt
Integrating both sides, we get:
ln|y| = 3t + C2
where C2 is another constant of integration. Exponentiating both sides, we have:
\(|y| = e^{(3t+C2) }= e^{C2} e^{(3t)\)
Since \(e^C2\) is just another constant, we can write:
y = ± \(Ce^{(3t)\)
where C is a constant.
The general solution to the system of differential equations dx/dt = 9, dy/dt = 3y is:
\(x(t) = 9t + C1\\y(t) = Ce^{(3t)} or y(t) = -Ce^{(3t)\)
where C and C1 are constants of integration.
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Question
find the general solution of the system of differential equations dx/dt = 9
dy/dt = 3y
A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the
probability of a tornado is 0.15.
. The number of tornadoes in any calendar year is independent of the number of tornados in any other
calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 19 year period.
Answers
Answer:
.441320612
or
44.132%
Step-by-step explanation:
This is binomial
fewer than 3 is equal to p(0)+p(1)+p(2)
\(p(0)={19\choose0}*.15^0*(1-.15)^{19}=.045599448\\p(1)={19\choose1}*.15^1*(1-.15)^{18}=.152892268\\p(2)={19\choose2}*.15^2*(1-.15)^{17}=.242828896\\p(0)+p(1)+p(2)=.441320612\)
When the town of Manning first started its voluntary recycling program, 2500 of the town's residence participated. The town predicts that the number of people participating in the recycling program will increase by 5% each year.
Which explicit rule can be used to determine the number of people participating in the program in the fifth year?
A. An=2500(0. 05)^n
B. An=2500(1. 05)^n-1
C. An=2500(0. 05)^n-1
D. An=2500(1. 05)^n
Answers
In this equation, A(n) represents the number of people participating in the program in the nth year.
To find the number of people participating in the fifth year, we substitute n = 5 into the equation:
A(5) = 2500 * (1.05)^(5-1)
A(5) = 2500 * (1.05)^4
This equation calculates the number of participants by starting with the initial number of participants (2500) and multiplying it by a growth factor of 1.05 raised to the power of (n-1). Since we want to determine the number of participants in the fifth year, we substitute n = 5 and obtain the desired result.
Patrick is x years old . His brother is 9 years older than he is .If his brother is y years old, express y in terms of x
Answers
Answer:
y = x + 9 ( in years)
Step-by-step explanation:
Given that Patrick is x years old and his brother is 9 years older than he is. Then;
His brother's age will be
= x + 9
If his brother is y years old then
y = x + 9
Since y is the subject, y has been expressed in terms of x. Where y is the age of Patrick's brother and x is Patrick's age.
A factory process requires 3 steps to finish a product. The steps each have a mean completion time of
= 10 seconds and a standard deviation of g = 5 seconds. The time it takes to complete each step is
independent from the other steps. Let T be the total completion time of the 3 steps on a randomly chosen
product.
Find the mean of T.
HT=
seconds
Use a whole number.
Answers
Answer:
square root 75
Step-by-step explanation:
khan
Using the normal distribution, the mean of T is of 30 seconds.
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
\(X \sim N(\mu, \sigma)\)
\(Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)\)
The mean of T is 10 seconds
A normal distribution has two parameters: Mean and standard deviation .
The given parameters are the mean completion time of each step, μ = 10 seconds
The standard deviation, σ = 5 seconds.
For the total completion, there are 3 instances, hence ,n = 3(10)
Thus, the mean of T is of 30 seconds.
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PLEASE ANSWERE ASAP
In △XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ.
AC = 7, AB = 5, and XY = 24. What is the perimeter of △XYZ?
Enter your answer in the box.
Answers
Answer:
AB = ½XZ. XZ = 5*2=10. (The middle line of the triangle)
AC = ½YZ. YZ = 7*2=14. The middle line of the triangle)
XY+YZ+XZ=P. P=110+14+24.P=48
Step-by-step explanation:
20 POINTS IF YOU GET THIS I NEED HELP
Answers
Answer:
sum=3.2559347
Step-by-step explanation:
product= 2x6x2 798.364
did it on edginuty and got it right
Math question please help urgently
Answers
Answer:
0, negative 9 and your welcome
A radioactive substance has an initial mass of 475 grams and a half-life of 20 days. What equation is used to determine the number of days, x, required for the substance to decay to 63 grams?
Answers
The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60
To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:
N(t) = N₀ * (1/2)^(t/h)
Where:
N(t) is the remaining mass of the substance at time t
N₀ is the initial mass of the substance
t is the time elapsed
h is the half-life of the substance
In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:
63 = 475 * (1/2)^(x/20)
To solve for x, we can isolate the exponential term on one side of the equation:
(1/2)^(x/20) = 63/475
Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:
log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)
By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:
x/20 = log(base 1/2) (63/475)
Finally, we can solve for x by multiplying both sides of the equation by 20:
x = 20 * log(base 1/2) (63/475)
Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:
x ≈ 20 * 4.1802
x ≈ 83.60
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The vertices of triangle EFG are E(-3, 2), F(-3, 0), and G(0, 0). The
triangle will be reflected over the x-axis. What will be the vertices of the image triangle?
A. E'(-2, -3), F'(0, 3), G'(0, 0)
B. E'(-3, -2), F'(-3, 0), G'(0, 0)
C. E'(3, 2), F'(3, 0), G'(0, 0)
D. E'(2,3), F'(0,3), G'(0, 0)
Answers
Answer:
B. E'(-3, -2), F'(-3, 0), G'(0, 0)
Step-by-step explanation:
When a point (x, y) is reflected over the x-axis the new coordinates will be
(x', y') where x'x = x and y' = -y
In other words, the transformation is
(x, y) ⇒ ((x, -y)
Point E is (-3, 2) . When transformed e' becomes (-3, -2)
The only choice where E' is (-3, -2) is choice B
You can test the others if you wish
Answer:
B. E'(-3, -2), F'(-3, 0), G'(0, 0)
A shipping company claims that 90% of its packages are delivered on time. Jenny noticed that out of the last 10 packages shipped, 2 were late. What is the probability that 2 out of 10 randomly selected shipments would be late?
Answers
Answer:
The probability is;
0.0000003645
Step-by-step explanation:
The probability of packages being early p is 90% = 0.9
The probability of packages being late q will be 1-p = 1-0.9 = 0.1
So the probability of 2 out of 10 random late will be subject to Bernoulli approximation of the Binomial theorem
That will be;
P(X = 2) = 10 C 2 0.9^2 0.1^8
= 0.0000003645
Answer:
0.19
Step-by-step explanation:
took the quiz
Given a graph for the transformation of f(x) in the format g(x) = f(kx), determine the k value.
Two parabolas open up with f of x passing through negative 3 comma negative 3 and g of x passing through negative 1 comma negative 3
k = negative one third
k = one third
k = −3
k = 3
Answers
k = 1/3 when two parabolas open up with f of x passing through negative 3 negative 3 and g of x passing through negative 1 negative 3.
How is the value of k determined by the given details of the graph?We must consider how the graph of f(x) gets transformed into the graph of g in order to determine the k value for the transformation of f(x) in the format g(x) = f(kx).(x). The vertex of a parabola is its lowest or highest point, depending on whether it is opening up or down, thus we can use the vertex coordinates of f(x) and g(x) to get the k value.
We know the vertices of both parabolas will be the lowest points on each graph because they both open up. Given that g(x) goes through and f(x) passes through (-3, -3), (-1, -3). We stretch or compress f(x) horizontally by a factor of k to convert it to g(x).
The x-coordinates of the parabolas' vertices can be used to determine k because it is where the horizontal compression takes place. The vertex of the quadratic function, f(x), has an x-coordinate of -b/2a, where b and an are its coefficients. Because f(x) is a parabola that is widening up in this instance, an is positive and the vertex's x-coordinate is -(-6)/(2*1) = 3. We can utilize this information to solve for k because the vertex of g(x) has an x-coordinate that is also 3k:
-1 = 3*k*(-3)
-1 = -9k
k = 1/9
Therefore, k = 1/3 is the right response.
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find a polynomial function f(x) of least degree having only real coefficients and zeros as given. assume multiplicity 1 unless otherwise stated.
Answers
a polynomial function f(x) of least degree with real coefficients and the given zeros (1 with multiplicity 1, 2 with multiplicity 2, and i) is:
f(x) = x^5 - 5x^4 + 9x^3 - 8x^2 + 4x - 4.
To find a polynomial function f(x) of the least degree with real coefficients and given zeros, we can use the fact that if a is a zero of a polynomial with real coefficients, then its conjugate, denoted by a-bar, is also a zero.
Let's consider an example with given zeros:
Zeros:
1 (multiplicity 1)
2 (multiplicity 2)
i (complex zero)
Since we want a polynomial with real coefficients, we need to include the conjugate of the complex zero i, which is -i.
To obtain a polynomial function with the given zeros, we can write it in factored form as follows:
f(x) = (x - 1)(x - 2)(x - 2)(x - i)(x + i)
Now we simplify this expression:
f(x) = (x - 1)(x - 2)^2(x^2 - i^2)
Since i^2 = -1, we can simplify further:
f(x) = (x - 1)(x - 2)^2(x^2 + 1)
Expanding this expression:
f(x) = (x - 1)(x^2 - 4x + 4)(x^2 + 1)
Multiplying and combining like terms:
f(x) = (x^3 - 4x^2 + 4x - x^2 + 4x - 4)(x^2 + 1)
Simplifying:
f(x) = (x^3 - 5x^2 + 8x - 4)(x^2 + 1)
Expanding again:
f(x) = x^5 - 5x^4 + 8x^3 - 4x^2 + x^3 - 5x^2 + 8x - 4x + x^2 - 4
Combining like terms:
f(x) = x^5 - 5x^4 + 9x^3 - 8x^2 + 4x - 4
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4/7 - -3/5 step by step pls explain
Answers
Answer:
41/35
Step-by-step explanation:
Simplify the following:
4/7 + 3/5
Put 4/7 + 3/5 over the common denominator 35. 4/7 + 3/5 = (5×4)/35 + (7×3)/35:
(5×4)/35 + (7×3)/35
5×4 = 20:
20/35 + (7×3)/35
7×3 = 21:
20/35 + 21/35
20/35 + 21/35 = (20 + 21)/35:
(20 + 21)/35
| 2 | 1
+ | 2 | 0
| 4 | 1:
Answer: 41/35
Which expression is the same as 2 (4-7m)?
A) 6-9m
B)6+9m
C)8-14m
D)8+14m
Answers
Answer:
The answer would be c) 8-14m
Answer:
C: 8-14m
Step-by-step explanation:
2(4-7m) = 8 - 14m
find this by distributing the 2 into the parenthesis: 2 * 4 and 2* -7m to get 8 and -7m
Junior's family is making mini pizzas. They have 35 pieces of pepperoni. if they put 6 pieces of pepperoni on each pizza, how many pizzas can they make? will they have any leftover pepperoni? (Long division)
Answers
Answer:
5
Step-by-step explanation:
35/6=5.83 round down and you get five
Find the slope of each line in the figure.
Slope of p =
Slope of q =
Slope of r =
Slope of m =
Slope of n =
Answers
Answer:
slope of p= -7/12
slope of q= -3/6.8
slope of r= -16/6.4
slope of m= 6.2/15.5
slope of n= 6.8/17
Step-by-step explanation:
The slopes of the line are given as 2.5 for p and q and -2.5 for r, m and n respectively.
What is the slope of straight line?The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.
The negative slope indicates the rate of decrease while the positive shows the rate of increase.
The slope of the given lines can be obtained as follows,
(a) In order to find slope of line p,
Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,
m = (-3 - 8)/(0.4 - (-4))
⇒ m = -2.5
(b) In order to find slope of line q,
Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,
m = (13 - 0)/(6.8 - 12)
⇒ m = -2.5
(c) In order to find slope of line r,
Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,
m = (13 - (-3))/(6.8 - 0.4)
⇒ m = 2.5
(d) In order to find slope of line m,
Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,
m = (-15.5 - 0)/(0 - 6.2)
⇒ m = 2.5
(e) In order to find slope of line n,
Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,
m = (-5 - 12)/(- 6.8 - 0)
⇒ m = 2.5
Hence, the slopes of first two lines are 2.5 and of the remaining three are 2.5.
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A population of 350 animals has a growth rate of 5% each year. Write a exponential function to model the situation.
Answers
Answer: A =350 (1.05)^t
Step-by-step explanation:
Hi, to answer this question we have to apply an exponential growth function:
A = P (1 + r) t
Where:
p = original population
r = growing rate (decimal form; 5/100=0.05)
t= years
A = population after t years
Replacing with the values given:
A = 350 (1+0.05)^t
A =350 (1.05)^t
Feel free to ask for more if needed or if you did not understand something.
What is the hypotenuse of a right triangle if the legs are each 20 inches long? Round to the nearest whole number.
A. 28
B. 29
C. 30
D. 31
Answers
Answer:
ueidicjfkfktitorr*rtt
28
Answer:
A
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is
h² = 20² + 20² = 400 + 400 = 800 ( take the square root of both sides )
h = \(\sqrt{800}\) ≈ 28 in ( to the nearest whole number )
What is the solution to this inequality?
x/12 + 3 < 7
OA. x≤ 48
OB. x≤ 81
OC. x ≥ 48
O D. x≥ 81
Answers
x/12 + 3 < 7 = x<48 this is the only one i can do because i cant do the others sorry
How many minutes to run 1 mile?
Answers
Answer:
I think that it's 6 minutes but I'm not sure
Answer:
Step-by-step explanation:
which of the following vectors is perpendicular to 〈2, −1, 3〉?
Answers
To find a vector that is perpendicular to another vector, we can take the cross product of the given vector and any non-zero vector. The resulting vector will be perpendicular to the original vector. In this case, we are given the vector 〈2, -1, 3〉, and we need to find a vector that is perpendicular to it.
To find a vector perpendicular to 〈2, -1, 3〉, we can take the cross product of this vector with any non-zero vector. The cross product of two vectors, say vector A and vector B, is a vector that is perpendicular to both A and B.
Let's choose a non-zero vector, say 〈1, 0, 0〉, and take the cross product with 〈2, -1, 3〉:
〈1, 0, 0〉 × 〈2, -1, 3〉
The result of the cross product will give us a vector that is perpendicular to both 〈2, -1, 3〉 and 〈1, 0, 0〉. We can calculate this cross product to find the desired vector.
The resulting vector will be perpendicular to 〈2, -1, 3〉. It's important to note that there are infinitely many vectors that are perpendicular to a given vector, as long as they are non-zero and not collinear with the original vector.
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what is the y-value of the solution to the system:{3x+4y=-6,5x+2y=4
Answers
Answer:
y = -3
Step-by-step explanation:
3x + 4y = -6 then, 3x = -4y - 6, x = (-4y - 6)/3
5x + 2y = 4
substitute for x:
5(-4y - 6)/3 + 2y = 4
simplify:
(-20y - 30)/3 = 4 - 2y
-20y - 30 = (3)(4 - 2y)
-20y - 30 = 12 - 6y
-14y = 42
y = -3
check:
5x + 2(-3) = 4
5x = 10
x = 2
3(2) + 4(-3) = -6
6 - 12 = -6
-6 = -6
5(2) + 2(-3) = 4
10 - 6 = 4
4 = 4
Is x - 1 factor of 7x ^ 3 - x ^ 2 - x - 5 ?
Answers
Answer:
Step-by-step explanation:
f(x) = 7x³ - x² - x - 5
To test if (x-1) is a factor, calculate f(x) for x=1:
f(1) = 7·1³ - 1² - x - 5 = 0
Since f(1) = 0, (x-1) is a factor.
Since Each baseball game has 162 games in 1 season how many games are in 22 seasons?
Answers
Answer:
3564 games
Step-by-step explanation:
multiply 162 by 22.
Answer:
3,564
Step-by-step explanation:
Find the exactar (optis 10 10 BR pl 2 Find the area hint the square is one unit of area)
Answers
The exact area of a square with a side length of 1 unit is 1 square unit. This means that the square completely occupies an area equivalent to one unit of area.
To find the area of a square, we need to square the length of one of its sides. In this case, the given square has a side length of 1 unit. When we square 1 unit (1²), we get a result of 1 square unit. This means that the square covers an area of 1 unit². Since the square has equal sides, each side measures 1 unit, resulting in a square shape with all four sides being of equal length. Therefore, the exact area of this square is 1 square unit
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what is the solution of 10(w +3) = 70
Answers
Answer:
w = 4
Step-by-step explanation:
distribute 10(w+3)=70
10w + 30 = 70
subtract 30
10w = 40
divide by 10
w = 4
Answer: w=7
Step-by-step explanation: 10 times what equals 70? 10 times 7 equals 10. So 3 plus 4 equals 7.
10(7+3)=70
DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD. If the area of the parallelogram is 1470 cm2 , AB=35cm and AD=49cm, Find the length of BM and DL.
Answers
Answer:
BM = 30 cm, DL = 42 cm
Step-by-step explanation:
The area of the parallelogram = 1470 cm², AB = 35 cm, AD = 49 cm, DL and BM are the heights on sides AB and AD.
area of the parallelogram = base × height = AD × height of AD = AD × BM
⇒ 1470 cm² = 49 cm × BM
BM = 1470 cm² / 49 cm = 30 cm
BM = 30 cm
Also:
area of the parallelogram = base × height = AB × height of AB = AB × DL
⇒ 1470 cm² = 35 cm × DL
DL = 1470 cm² / 35 cm = 42 cm
DL = 42 cm
2. A box of 25 lightbulbs is shipped to a hardware store,
When it arrives 3 of the bulbs are broken. The hardware
store will order 100 more lightbulbs, which prediction is best
supported by the data?
A. There will be 3 broken bulbs in the shipment
B. There will be 12 bulbs that are not broken
C. There will be 12 broken bulbs
D. There will be 3 bulbs that are not broken
Answers
Answer:
c
Step-by-step explanation:
3/25 is equivilant to 12/100, which means that there will most liky be 12 bulbs broken out of 100
pls mark brainliest
hope it helps