Consider square matrices A & B where A#0, B#0,AB=0. Show that |A|=0 or |B|=0.

Q: Let A and B be square matrices of order 4 such that |A| = -4 and |B| = -4. Find the following. (a)…

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Q: Let A and B be square matrices of order 3 such that ∣A∣ = −2 and ∣B∣ = 5. Find (a) ∣BA∣, (b) ∣B4∣,…

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Q: Write B as a linear combination of the other matrices, if possible. (If not, enter DNE in all…

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Q: Given the matrices X + A = B. A =

A: Given that -1/3X+A=B

Q: Use the fact that matrices A and B are row-equivalent. 2 1 2 5 1 7 2 1 A = 2 -2 7 15 6 -1 3 0 -4 0 1…

A: The given matrix is                          A=12100251103722-27156-14 and B=1030-401-1020001-200000…

Q: Q2: Let A, B be matrices of size 3x3 such that and AB = A+2I A = -101 21 2 find A, B?

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A: Given, A=abcdD=ad-bc≠0

Q: Calculate BA where A and B are the following non-square matrices: 1 3 1 0 3 A = B = 2 %3D 2 1 5 2

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Q: Prove using elements that for any square matrices A,B of the same size and constant K.…

A: For any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

Q: Use the matrix P to determine if the matrices A and A' are similar. 6 0 0 6 12 0 P =|0 5 0 0 0 2 6…

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Q: Determine whether the matrices A and B are equal.

A: Given two matrices are: A=1-201260 and B=1-2126 To determine whether two matrices are equal.…

Q: Show that if A is a square matrix that satisfies the equation A2 -2A +I= 0, then A-1 = 2I -A.

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Q: Show AB + BA for the indicated matrices. A= 2 3] B = -1

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Q: Consider A and B are two square matrices and B is a scalar. Calculate (BA^T B)^(-1) = *

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Q: Find (A, B), ||A||, ||B||, and d(A, B) for the matrices in M2.2 using the inner product (A, B) =…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Find the product AB of two matrices. a) A = [1 2 0 -1 -1 .3 2

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Q: Use the fact that matrices A and B are row-equivalent. -2 -5 8 0 -17 -5 1 7 5 -43 1 3 A = -3 -5 7…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 2) Consider the matrices A= (;) (2) and B= (! %3D -/ 2 Calculate 2A +3B, AR, C0o d BA

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Q: -3 For the matrices A and B, verify that A.B=B.A, where A=[53] and B= 4 4 -51

A: Given :A=5443   and B=-344-5

Q: Use the fact that matrices A and B are row-equivalent. 1 2 1 5 1 2 A = 3 1 7 2 2 -2 11 25 8 -1 8 1 0…

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Q: Which of the following matrices are diagonalizable?

A: We know if the all eigenvalues of a matrix are distinct and equal  to order of the matrix .then…

Q: , and c

A: Given quadratic form is, Here, A is symmetric matrix as,

Q: Find (A, B), ||A||, |B|, and d(A, B) for the matrices in M2.2 using the inner product (A, B) =…

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Q: Find (A, B), ||A||, ||B||, and d(A, B) for the matrices in M2.2 using the inner product (A, B) =…

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Q: Use the matrix P to show that the matrices A and A′ are similar.

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Q: Find matrices P, D and P-1 that diagonalize matrix A, where A = P = D= P-1 20 0 -11 -2 -3 -30 -1

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Q: 43. For square matrices A and B, is it true, in general, that (A + B)-1 = A¯1 + B¯!? Explain.

A: Explanation of the answer is as follows

Q: Find a matrix B such that AB = I, where [ ] 8 1 1 0 A = and I = -8 8 0 1 1 a b Hint: Let B = %3D c d…

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Q: Let A and B be nx n matrices. Which of the following statements are always true? (i) (AB)² = 4²B?

A: i   AB2=A2B2-Not Trueii   Ax=0 has infinity many solution then A is not inversible .…

Q: Use the fact that matrices A and B are row-equivalent. 1 2 1 0 2. 5 1 1 A = 3 7 2 2 -2 10 23 7 1 1 0…

A: Show that matrix A and B are row equivalent.

Q: Find (A, B), ||A||, ||B||, and d(A, B) for the matrices in M2,2 using the inner product (A, B) =…

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Q: Show that if A is a square matrix that satisfies the equation A2 - 2A + I = O, then A-1 = 2I - A.

A: Given that,                    A2-2A+I=0

Q: Consider square matrices A & B where A#0, B÷0,AB=0. Show that |A|=0 or |B|=0. 6.

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Q: Find (A, B), ||A||, ||B||, and d(A, B) for the matrices in M2,2 using the inner product (A, B)…

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Q: Find the matrix X, such that XDC - 2XC — ХС? + С satisfies. 3 4 4 6 6 5 C = 1 2 1 D = 1 3 -2 4 -2 -4…

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Q: Let A and B be square matrices of order 4 such that ∣A∣ = −5 and ∣B∣ = 3. Find (a) ∣A2∣, (b) ∣B2∣,…

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Q: Use the matrix P to determine if the matrices A and A' are similar. -1 -1 15 9. 6. 2 P = -20 -14 0…

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Q: Use the fact that matrices A and B are row-equivalent. -2 -5 8 0 -17 1 -5 1 5 A = -5 -11 17 3 -53 1…

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Q: For all square matrices A and B, it is true that det(A + B) = det(A) + det(B) O True O False

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Q: For matrices A, B, and C, if A is invertible and AB-C, then True False B = CA-¹.

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Q: Find all a > 0 and B>0 so that the matrix 3 2 B A A =| a 5 B 1 is strictly diagonally dominant.

A: The given matrix,A=32βα5β21α

Q: Find (a) ⟨A, B⟩, (b) ||A||, (c) ||B||, and (d) d(A, B) for the matrices in M2,2 using the inner…

A: We need to find   (a) ⟨A, B⟩, (b) ||A||, (c) ||B||, and (d) d(A, B) for the matrices in M2,2 using…

Q: Let A and B be square matrices of order 4 such that ∣A∣ = 4 and ∣B∣ = 2. Find (a) ∣BA∣, (b) ∣B2∣,…

A: Let A and B be square matrices of order 4 such that ∣A∣ = 4 and ∣B∣ = 2. We need to Find (a) ∣BA∣,…

Q: Find the product AB, where A and B are the following matrices: 1 0 a 1 0. A 0 0 1 B = -1 0. 1 1 1

A: SOLUTION-

Q: Use the fact that matrices A and B are row-equivalent. 1 2 1 2 5 1 1 A = 3 7 2 2 -2 10 23 7 -2 10 1…

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Q: Consider the matrices A = and B c d Show how you use the dot product definition to calculate ONLY…

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Q: Find all 2 x 2 matrices A of the form a -4 A = %3D 9. where a and b are real numbers, such that =-A.

A: Given matrix is: A=a-41b A-1=Adj(A)A                       (1) Find determinant of matrix A |A|=ab+4…

Q: Show by counterexample that (AB)−1 ≠ A−1B−1. That is, find two matrices A and B for which (AB) -1 ≠…

A: Let