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Suppose that and B 4 -2 4 4 -2 2 Given the following descriptions, determine the...
(1 point) Suppose that 1 1 -2 5 5 2 145 Given the following descriptions, determine...
(1 point) Suppose that 1 1 -2 5 5 2 145 Given the following descriptions, determine the following elementary matrices and their inverses. matrix Ezi subtracts 5 times the first row of A from the second row of A E21 = The elementary matrix Ez1 subtracts -6 times the irst row of A from the second row of A The permutation matrix Piz switches the first and second rows of A P12 The elementary matrix Ezi subtracts 7 times the...
(1 point) Suppose that: -15 A= and B = 3 -2 -4 -1 5 e) The...
(1 point) Suppose that: -15 A= and B = 3 -2 -4 -1 5 e) The elementary matrix E2.1 subtracts 6 times the first row of B from the second row of B. E2,1 = , Ez1 = f) The elementary matrix E3.1 subtracts -5 times the first row of B from the third row of B. E3.1 = g) The permutation matrix P13 switches the first and third rows of B. P13= ,P3! = h) The elementary matrix E32...
Suppose that: A =[-4 2 -3 3] and B = [-5 -1 5 5 -1 4 -2 -2 -1] Given the following descriptions, determine the following elementary matrices and their inverses. {View Image}
a. The elementary matrix ?1E1 multiplies the first row of A by 1/6.b. The elementary matrix ?2E2 multiplies the second row of A by -4.c. The elementary matrix ?3E3 switches the first and second rows of A.d. The elementary matrix ?4E4 adds 6 times the first row of A to the second row of A.e. The elementary matrix ?5E5 multiplies the second row of B by 1/3.f. The elementary matrix ?6E6 multiplies the third row of B by -4.g. The elementary matrix ?7E7 switches the first and third rows of B.h. The elementary matrix ?8E8 adds...
(1 point) Suppose that: -4 -2 -1 -3 -3 A= 1 and B = -1 -3...
(1 point) Suppose that: -4 -2 -1 -3 -3 A= 1 and B = -1 -3 -1 -4 4 4 -3 -5 Given the following descriptions, determine the following elementary matrices and their inverses. e. The elementary matrix Es multiplies the second row of B by 1/2 Es = f. The elementary matrix Es multiplies the third row of B by -6. Eg = g. The elementary matrix E, switches the first and third rows of B. ,E,= h. The...
4. For the given elementary row operation e, find its inverse operation e-1 and the elementary...
4. For the given elementary row operation e, find its inverse operation e-1 and the elementary matrices associated with e and e-1, e = R 2 R, the e: Add - 2 times the second row to the third row of 3 x 3 matrices.
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A...
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A using the cofactor expansion technique along (a) row 1 and (b) column 3. (ii) In trying to find the inverse of A, applying four elementary row operations reduces the aug- mented matrix [A1] to -2 0 0 0 0 -2 2 1 3 0 1 0 1 0 -2 Continue with row reductions to obtain the augmented matrix [1|A-') and thus give the in-...
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If...
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If the matrix B is obtained from mes the second row to the first, then det(B) = 2. If the matrix C is obtained from A by swapping the first and second rows , then det(C) = 3. If the matrix D is obtained from A by multiplying the first row by 5, then det(D) =
13 please 8. b. -2 3 0 0 0 0 -1 2 0 0-4 0 3...
13 please
8. b. -2 3 0 0 0 0 -1 2 0 0-4 0 3 0-2 0 3 0 0 -2 0 3 0 4 o0-1 6 0 0 1 o 2 6 0 0 -1 6 10. For any positive integer k, prove that det(4t) - de(A)*. 11. Prove that if A is invertible, then den(A-1)- I/der(A) - det(4)- 12. We know in general that A-B丰B-A for two n x n matrices. However, prove that: det(A . B)-det(B...
2. Matrix A = Matrix B = log(A) Write MATLAB expressions to do the following. Evaluate...
2. Matrix A = Matrix B = log(A) Write MATLAB expressions to do the following. Evaluate the sum of the first row of B Evaluate the maximum value in the vector resulting from element-by-element multiplication of the first column of B with the third column of A. Use element-by-element division to divide the third row of A by the first three elements of the second column of B and evaluate the sum of the elements of the resulting vector.
Prove the following lemma. Let B be an n ✕ n matrix and let E be...
Prove the following lemma.
Let B be an n ✕ n
matrix and let E be an n ✕ n
elementary matrix. Then det(EB) = det(E)
det(B)
1. Write the proof and submit as a free response. (Submit a file
with a maximum size of 1 MB.)
2. Which of the following could begin a direct proof of the
statement?
If E interchanges two rows, then det(E) = 1 by
Theorem 4.4. Also, EB is the same as B but...
(1 point) Suppose that 1 1 -2 5 5 2 145 Given the following descriptions, determine the following elementary matrices and their inverses. matrix Ezi subtracts 5 times the first row of A from the second row of A E21 = The elementary matrix Ez1 subtracts -6 times the irst row of A from the second row of A The permutation matrix Piz switches the first and second rows of A P12 The elementary matrix Ezi subtracts 7 times the...
(1 point) Suppose that: -15 A= and B = 3 -2 -4 -1 5 e) The elementary matrix E2.1 subtracts 6 times the first row of B from the second row of B. E2,1 = , Ez1 = f) The elementary matrix E3.1 subtracts -5 times the first row of B from the third row of B. E3.1 = g) The permutation matrix P13 switches the first and third rows of B. P13= ,P3! = h) The elementary matrix E32...
(1 point) Suppose that: -4 -2 -1 -3 -3 A= 1 and B = -1 -3 -1 -4 4 4 -3 -5 Given the following descriptions, determine the following elementary matrices and their inverses. e. The elementary matrix Es multiplies the second row of B by 1/2 Es = f. The elementary matrix Es multiplies the third row of B by -6. Eg = g. The elementary matrix E, switches the first and third rows of B. ,E,= h. The...
4. For the given elementary row operation e, find its inverse operation e-1 and the elementary matrices associated with e and e-1, e = R 2 R, the e: Add - 2 times the second row to the third row of 3 x 3 matrices.
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A using the cofactor expansion technique along (a) row 1 and (b) column 3. (ii) In trying to find the inverse of A, applying four elementary row operations reduces the aug- mented matrix [A1] to -2 0 0 0 0 -2 2 1 3 0 1 0 1 0 -2 Continue with row reductions to obtain the augmented matrix [1|A-') and thus give the in-...
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If the matrix B is obtained from mes the second row to the first, then det(B) = 2. If the matrix C is obtained from A by swapping the first and second rows , then det(C) = 3. If the matrix D is obtained from A by multiplying the first row by 5, then det(D) =
13 please
8. b. -2 3 0 0 0 0 -1 2 0 0-4 0 3 0-2 0 3 0 0 -2 0 3 0 4 o0-1 6 0 0 1 o 2 6 0 0 -1 6 10. For any positive integer k, prove that det(4t) - de(A)*. 11. Prove that if A is invertible, then den(A-1)- I/der(A) - det(4)- 12. We know in general that A-B丰B-A for two n x n matrices. However, prove that: det(A . B)-det(B...
2. Matrix A = Matrix B = log(A) Write MATLAB expressions to do the following. Evaluate the sum of the first row of B Evaluate the maximum value in the vector resulting from element-by-element multiplication of the first column of B with the third column of A. Use element-by-element division to divide the third row of A by the first three elements of the second column of B and evaluate the sum of the elements of the resulting vector.
Prove the following lemma.
Let B be an n ✕ n
matrix and let E be an n ✕ n
elementary matrix. Then det(EB) = det(E)
det(B)
1. Write the proof and submit as a free response. (Submit a file
with a maximum size of 1 MB.)
2. Which of the following could begin a direct proof of the
statement?
If E interchanges two rows, then det(E) = 1 by
Theorem 4.4. Also, EB is the same as B but...
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