1. Prove or disprove. a) det(A + B) = det(A) + det(B) b) det(AB"A')= det B c) (A+B)(A – B) = A² – B', where A & B are n x n matrices %3D

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

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

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Q: b) Let A, B, C, DE RX" be invertible matrices and suppose A" = c" (A-' D)")" B. %3D Solve for D in…

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Q: Let A and B be two square matrices. Which of the following statement or statements are always…

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Q: 3. Show that (AB)* B' A' by using the matrices A and B giver [8 -2 5] 1 -5] B = 7 0 -3 A =1 -4 3 6.…

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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: (i) Use the definition of inverse to prove the following: if A and B are n × n nonsingular matrices,…

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Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 – 2xy – 2xz –…

A: Step:-1 Given quadratic form is  Q=2x2 +2y2 +2z2 -2xy -2xz -2yz Q=xyz 2-1-1-12-1-1-12 xyzQ=XTAXHere,…

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: 2. Let (r x s) denote an r x s matrix. Find the size of those matrix products that are defined. а)…

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Q: Let A be a 3 x 3 matrix such that det(A) = 2. Evaluate det(Aª) and det(2A).

A: Recall the following. If A is a n×n matrix and m be any positive scalardet k A=kndet Adet Am=det Am

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

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Q: 2. Consider the four matrices, 1 2 1 2 3 C = 4 5 6 1 2 3 4 3 A = 5 6 3 4 5 6 78 9 Solve for: а. АВ…

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Q: a- B-2 3] and Given matrices Find CAB 3

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Q: Find two non zero matrices A and B such that AB = 0. %3|

A: Find the two matrix which satisfy the given condition

Q: Let A and B be square matrices of order 3 such that |A-| = x + 7 with x + -7 and |A * A" | = . What…

A: A and B are square matrices. Therefore, det(AB)=det(A).det(B) det(A)=det((A)T) We will use these…

Q: a) Let A and B be two regular (nonsingular) (n, n)-matrices. Determine whether the following is…

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Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

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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: 2. Let (r x s) denote an r x s matrix. Find the size of those matrix products that defined. a) (2 x…

A: Matrix multiplication is possible only when number of columns in the first matrix is the same as the…

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

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Q: 5. Find the cofactors and the adjoint matrix of A where (1 1 -1 b) A =|2 3 7 0 -1 a) A =-2 0 -2 4 -3…

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Q: (8) Let A and B be m x n matrices. Prove that the rank of A + B is less than or equal to the rank of…

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Q: Let A and B be square matrices of order 2 such thatA=-7 and B=4.What is (ABY"| %3D %3D

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Q: side is the the (a) 1 (b) 3 Assume that (2,3, =) " where the left-hand product of two matrices. If…

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Q: 3. Let A and B be 4 x 4 matrices such that |A| = 4 and |B| = -2. Find (a) |AB| (b) |2B| (c) |A¹| (d)…

A: Solution:Given: Let and be matrices such that and we have to…

Q: Solve the matrix equation for X: -1 0 1 1 2 X 1 1 %3D -3 1 -1 3 1 -1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…