Consider the elementary matrices below. 1 For A = 0 0 det (A) = 1 0 0 For B = 0 k 0 0 0 1 det (B) = 1 For C = 0 0 0 0 0 1 1 0 det (C) = 0 0 1 k 01 Now if M is an arbitrary matrix with det (M) = 4, then det (BM) =

Q: Let A and B be A = 2 0 1 -3 2 1 -2 -1 0 E = B = -2 -1 0 0 2 1 2 1-3 Find an elementary matrix E such…

A:

Q: Let A be the matrix Find p(A). p(x) = x – 2x +4 i 5 i p(A) = i

A:

Q: Find i from the equation provided for the matrices. (AB)-Ct=D 4 - i 6i 2 - i 2 + 3i 3+ 2i 5 + 3il 0…

A: AB-CT=DFirst, find AB=?AB=4-i6i32-i2+3i3+2i-4i5+3i1052-13      =…

Q: Determine whether the following matrices are in reduced echelon form. If a matrix is not in reduced…

A:

Q: Find the elementary matrix E such that EC = A where 2 1 5 2 1 A = 3 0 -1 and C- 3 Communest 0 6 -8 2…

A:

Q: Compute AB, det(A), det(B), det(AB), and det(A + B) for the following matrices. 1 0 -1 4 0 5 0 1 A =…

A: Given that :- A=50113-1101 , B=10-1401010 find AB,detA,detB,detAB,detA+B

Q: 1) Consider the matrix A = −1 102 020 004 . (i) Compute the inverse of A. (ii) Write A as a product…

A:

Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

A: Given that .The objective is to express the matrix  as a product of elementary matrices.

Q: Use the following matrices and find an elementary matrix E that satisfies the stated equation. 1 1 5…

A: The details solution is given below in step 2.

Q: 10. Let - 2 1 0 A=| 0 4 3 1 (a) Find elementary matrices E3 E,E,A = I3 (6) Express A as a product of…

A:

Q: If 1  0  0  0 is a diagonal matrix    0  1  0  0     0  0  1  0      0  0  0  1    So, is  0  0…

A:

Q: Consider the matrices below.(a) Find scalars a, b, and c such that W = aX + bY + cZ. (b) Show that…

A: The given vectors are X=1201, Y=-1032, Z=34-12, W=32-4-1 a We have to find the scalars a, b, and c…

Q: Yes No No Yes No Which of the following matrices are orthogonal? -1 0 01 0 0 0 1. 0 1 2. 3. 4. 1 21…

A:

Q: 4s – r – 5t - (2r + 5s + 3t) 4t – (4r + 4s) 5s – 3r + 3t with r, s and t real. Find a matrix A such…

A: Let's find.

Q: Express the matrix and its inverse as products of elementary matrices. 10-4 A =0 8 6 0 01

A: A = 1 0 -4 0 8 6 0 0 1 Here expressing A as a product of elementary matrices we get ,…

Q: [1 2 1 Given that matrix A= |1 -1 0, find the matrix A². If A³ – A² – 6A = I %3D |3 1 1 where I is…

A:

Q: Find the adjoint of the matrix A. Then use the adjoint to find the inverse of A (if possible). (If…

A:

Q: .

A:

Q: Express the matrix and its inverse as products of elementary matrices. 10-6 i 7 1 A = 0 9 00 The…

A: Let us go by one option by one to find the solution. First option:…

Q: For each of the following matrices A, find an invertible matrix QE M₂ (R), a positive real numbers,…

A:

Q: If A = a b c d then A is invertible if ad - bc # 0, in which case A-1 1 d -b ad-bc-c a If ad bc = 0,…

A:

Q: Find an invertible matrix P and a diagonal matrix D such that P-¹AP=D. -1 0 0 0 92-18 0 0 0 -1 0 000…

A: Please find attachment

Q: Find an invertible matrix P and a diagonal matrix D such that P-¹APD. 1 -8 20 A = 0 9 -20 04 -9 000…

A: We know that a diagonal matrix is a square matrix whose diagonal entries are non-zero and all the…

Q: Find the ranks of the following matrices. 0 3 0 0 -4 0 rank 1 0 0 0 1 0. rank 0 -2 3 1 rank 8. || 3.…

A:

Q: 1 2 3 Let A = 5 1 Find 3x3 matrices X and Y such that A = XY -YX. %3D 1 1 -2

A: Given that X,Y are square matrix of order 3. If  X=aij3×3 and Y=bij3×3 Then, tr X=∑i=13aii and tr…

Q: 17. Let A and B are similar matrices, that is, A = P-¹BP for some invertible matrix P. Then, prove…

A:

Q: Let A be the matrix 4 2 7 6 Find p(A). p(x) = x – 2x + 4 i i p(A) =

A:

Q: Let [5 -3] A = [1 -3 – 2k] В — k 6+ 5k Find the elementary matrices E, and E2such that B = E2E¸A.…

A: An elementary matrix is a matrix which differs from the identity matrix by one single elementary row…

Q: 3. Зx-4y+6-0 and 2x-5y-19-0 ans.A [5 4 – 23]

A: