Homework Answers
(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...
Suppose that and B 4 -2 4 4 -2 2 Given the following descriptions, determine the...
Suppose that and B 4 -2 4 4 -2 2 Given the following descriptions, determine the following elementary matrices and their inverses. a) The elementary matrix E subtracts 5 times the first row of A from the second row of A. Ei- b) The elementary matrix E21 subtracts -3 times the first row of A from the second row of A. Ei- c) The permutation matrix P12 switches the first and second rows of A. 12 d) The elementary matrix...
(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...
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 A is a 3 × 3 matrix. For each of the question...
(1 point) Suppose that A is a 3 × 3 matrix. For each of the question a A after the given row operation is performed. Then give E-1 d), find the elementary matrix E such that EA gives the matrix resulting from
Question 1 a. Define the following matrices in a script file (M-file), ? = ( 8...
Question 1 a. Define the following matrices in a script file (M-file), ? = ( 8 9 10 11; 23 9 16 15 ;11 12 3 6; 1 2 8 9 ) ? = ( 2 21 7 15; 12 4 8 22; 23 9 5 13; 23 4 21 22) ℎ = (4 9 12 15) b. Add suitable lines of codes to the M-file to do the following. Each of the following points should be coded in only...
(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) =
(1 point) Suppose that we have 5 matrices A a 3 x 2 matrix, B a...
(1 point) Suppose that we have 5 matrices A a 3 x 2 matrix, B a 2 x 3 matrix, C a 4 x 4 matrix, D a 3 x 2 matrix, and Ea 4 x 4 matrix. Which of the following matrix operations are defined? A. A+D B. C+E C. 3C - 6D D. 4E-6D E. 4D + A F. 3A G. C+E+D H. 4B L. A + B
(1 point) Assume that A is a matrix with three rows. Find the elementary matrix E...
(1 point) Assume that A is a matrix with three rows. Find the elementary matrix E such that E A gives the matrix resulting from A after the given row operation is performed. R2 R3 E=
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...
(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...
Suppose that and B 4 -2 4 4 -2 2 Given the following descriptions, determine the following elementary matrices and their inverses. a) The elementary matrix E subtracts 5 times the first row of A from the second row of A. Ei- b) The elementary matrix E21 subtracts -3 times the first row of A from the second row of A. Ei- c) The permutation matrix P12 switches the first and second rows of A. 12 d) The elementary matrix...
(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...
(1 point) Suppose that A is a 3 × 3 matrix. For each of the question a A after the given row operation is performed. Then give E-1 d), find the elementary matrix E such that EA gives the matrix resulting from
(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) =
(1 point) Suppose that we have 5 matrices A a 3 x 2 matrix, B a 2 x 3 matrix, C a 4 x 4 matrix, D a 3 x 2 matrix, and Ea 4 x 4 matrix. Which of the following matrix operations are defined? A. A+D B. C+E C. 3C - 6D D. 4E-6D E. 4D + A F. 3A G. C+E+D H. 4B L. A + B
(1 point) Assume that A is a matrix with three rows. Find the elementary matrix E such that E A gives the matrix resulting from A after the given row operation is performed. R2 R3 E=
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...
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