Consider the matrices 3 0] -1 2 1 1 [1 4 2] A= B= C= 3 1 5 15 2] -1 0 1 3 2 4 6 1 3] D= E = -1 1 2 4 1 3] Using these five matrices, please calculate the following (when possible), showing sufficient "ork: a) 7A b) B+C c) 2D - E d) A-A e) tr(D) f) tr(E-3D) 9) B-B" h) 늘d+ A

Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix 2x + y + 3z = 1     y + z…

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Q: - ; Let A be a square matrix such that A? – 7A+ 81 = 0 (where I and 0 are the identity and zero…

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Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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Q: 4. Consider the matrices U = V = 2 -3 Calculate the following, where legal: (a) 4U (b) UUT (c) UV

A: Here the given matrices are                                             U=110-2   and V=012-311…

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Q: or the giren m diaey that ( RS)*=5"" and UEP)e = p*t matrices, yenfy 2. E = 3-2i 273i 41 i P=1-i --…

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Q: Find matrices A and B in M2(Z) such that AB= 0, but BA+0. 3.

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A: Given that A =1000-10001B=10000000-1 and C=0-i0i0i0i0We need to find Tr (ABC)T.First of all we…

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Q: State Cayley-Hamilton theorem and prove this for following matrix [1 1 A 1 2 -1 %3D [5 8

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Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix x + y - z = 1      x+y+z=2…

A: The coefficient matrix is, Now,

Q: Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is symmetric,…

A: Given that B=QRQ-1 where, Q is orthogonal and R is upper triangular. Then, multiply Q on both sides:…

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

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Q: If the n x n matrices A and B are symmetric and B is in- vertible, which of the matrices in…

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A: The objective is to prove that

Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix x + y = 1   x-y=2

A: x+y=1 x-y=2 We need to find the inverse using A-1 =(1/detA)adj A

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Q: (b).Use the matrices а A d and 5 3 В 4 7 to illustrate Det AB Det BA det A. det B.

A: The matrix AB and  BA are:…

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Q: 1. Let A = [a;j]4x5, B = [bij]4x5; C = [cij]5x2; D = [d:j]4x2, and E which of the following matrix…

A: Matrix addition: Let A be an m×n matrix and B be an also m×n matrix. A= {aij: 1≤i≤m ; 1≤j≤n} and B=…

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Q: 2rị + 13 T: R' → R?, T 21, 22, 13, L4 ER -12 - 3r4

A: Given  and the standard bases are given by

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A: A be a 2×3 matrix. This means A2×3 . entries of matrix A are ai,j=(i-1)(j+1)

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Q: Given that matrices A and B O 2] A = |1 0 2 lo o 1] [o o 21 [o 2 and B = 0 Lo 1 01 Where 1 2 3. Find…

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Q: 1 1 1 1 4 1 1 1 1 1 1 0 1 2 1 1 3 20 1 4 1 0 1 1 3 3 2 3 3 2 3 3 4 1 3 1 1 3 1 1 1 1 3 A = B = C = 1…

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Q: Suppose A is a 2 x 2 matrix such that for all x, y E R², (Ax) · (Ay) = x ·y Must it be true that A…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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A: Let's find.

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Q: 5. Find three 2 x 2 nonzero matrices A, B and C such that B C and AB = AC = 0.

A: To find the matrices A, B and C satisfying the given conditions.

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Q: Let A, Band C be square matrices Such that AB = AC, If A#0,then B-C. 1s this True or false? Explain…

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