1. Prove the following for any two matrices A and B of order ( 2 × 2 ). (A + B)² = A² + AB + BA + B2 а.

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

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Q: Let A = 2 1 54 Write 5A. Is det(5A) equal to 5det(A)? 5A= (Type an integer or decimal for each…

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Q: Assuming that all matrices are n x n and invertible, solve for D. CABT DACTB = CAT.

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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: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

Q: Consider the two matrices: 2 4 1 -5 A = B = 2 Compute A + 3 B. The result is equal to: Select one:…

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Q: -3 4 B = -1 | %3D 4 | 0 4 3. C = -2 5 1 D = 4 -2 0 1 Using the above matrices find DB

A: Given matrices are

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, 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: o matrices A and B one has that Null(B) is contained in Null(A · B).

A: Given, for two matrices A and B, to show that Null (B) contained in Null(A·B).

Q: Let A and B be unitarily equivalent complex matrices. Show that A is normal if and only if B is…

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Q: [1 3 B = 2 1 5 0 A = 0 -5 4 and 3 8 QA + B'.

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Q: a) Suppose that A and B are 4 x 4 matrices, det(A) = 2 and det((3ATB)-¹) = . Calculate det(B). b)…

A: As per our company guideline we are supposed to answer only one question kindly post remaining…