Find  A, B  ,   A  ,   B  , and d(A, B) for the matrices in M2,2 using the inner product  A, B   = 2a11b11 + a21b21 + a12b12 + 2a22b22

Q: Suppose that matrix A has dimension 2x2 and that matrix B has dimension 2x5. Decide whether the…

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Q: Determine which of the following identities are true for all 2x2 matrices A, B, C. (Select all that…

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Q: Find the LU factorization of -1 -5 -4 A = -5 -26 -18 That is, write A = LU where L is a lower…

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Q: 3.) Prove (cA)" = cCA) %3D

A: Let A be a m×n matrix so A=(aij)  1≤i≤m and 1≤j≤n ie A has m rows and n columns. By AT we mean…

Q: Suppose that matrix A has dimension 5•3 and that matrix B has dimension 3•5. Decide whether product…

A: Given: The matrix A has dimension 5×3 and that matrix B has dimension 3×5. To Find: To decide…

Q: Find two 3 x 3 matrices A and B such that det(A + B) + det(A) + det(B)

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Q: Determine all 2 × 2 matrices A such that AB = B A for any 2 × 2 matrix B.

A: Let A=abcd and B=pqrs be any 2×2 matrices.

Q: (A, B), ||A||, |B||, and d(A, B) for the matrices in M2,2 using the inner product (A, B) = 2a11b11 +…

A: 1) <A,B>=2*2*(-3) +(-1)*1 +(-5)*1+2*3*0                    =-12-1-5                     =-18…

Q: Find the following matrix product. Be careful to distinguish 2 × 2 matrices in the answers from 2 x…

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Q: Let A and B be 3 × 3 matrices such that det (B) = -2 and 27 = det (-3AB A" B ²). 2 Find det(A).…

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Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

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 following matrix product. Be careful to distinguish 2 x 2 matrices in the answers from 2 x…

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Q: -4 -2 (1 point) If A = 1 2 - 3 and B -2 1 4 then -4 1 4 -3 -4 4 AB = and ВА — Choose v True or…

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Q: Let H be the collection of all 2 × 4 matrices whose second and fourth columns are equal. Show that H…

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Q: D = A= = Γ1 0 0 0 01 00 00 10 00 4 π 0 √2 23140 3 0 1 1 E = 27 0 5 0 0 0 √2 0 00 10 001 F = [100 0]…

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Q: Given two nxn matrices A and B, what are the criteria for the matrices to be inverses?

A: Given the matrices A and B of order nxn.

Q: Select all of the following that are true for all nxn matrices A and B. AA²-A²A (A+BILA-B)-A²-B²…

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Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

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Q: Let A, B be 4 x 4 matrices. Find two matrices so that rank(A) = rank(B) = 2 and rank(AB) = 1. A = B…

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Q: Show by direct calculation for 2x2 matrices A, B, C that A(BC)

A: To prove that  for 2×2 matrices A, B,  that A(BC)=(AB)C.

Q: Explain why det (BPB¯¹) = det(P) for any matrices P and B. Assume both sides of the equation are…

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