1. 2. 3. Given A = 3 -1] 4 7 Given X = and B= 1 -2] [10 31 Show that (X+Y)(X-Y)# X²-Y² 1 [ and Y= 1 1 Given the matrix D= 2 -3 4 3 -2 -2 Determine AB and BA. -3 1 2 - find the inverse matrix of D.

Q: 4. Consider the matrix 1 0 0 0 0 0 -2a -a (a² + a) 0 (2-a²) - (2-a²) -2a (2-a²) 2+ 4a - a² Find all…

A: 4) Solution:According to the given data, find the all values of a for which given matrix is psd.

Q: 9. 4 -6 -21 7 3. 8 -3 4 -7 8 8 0 13 17 31 7 9 4 23 4. -6 11 0 3 6 0

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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: what value is in the 2nd row 2nd column of V x 3Q [3 4 -31 Г2 3 V = |0 -1 Q = 18 5 %3D 12 -2 1 1 5…

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Q: Find the matrix product AB, if it is defined. 1 0 2 - 2 A = 0 3 B = 2 -2 2.

A: Given, A = 1003  B = 32-22-22  We have to find the product matrix AB.

Q: 5. Let D be a non-singular matrix such that 7. (7D)- 1 -2 Find D.

A: Inverse matrices

Q: 12.) Find the determinant of A= -2 3 1 57 -1 2 0 4 1 0 TN -2 1 3 -3 4 Show your work.

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Q: Q9. As usual, let In denote the n x n identity matrix. 1 - (a) Find a 2 × 2 matrix such that A² =…

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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: 1. Find the inverse of each matrix using the adjoint matrix. (2 1 5) b) B = 3 0 1 1 2 1 (2 -5 -3 a)…

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Q: 7) Find the determinant of the following matrices: -51 6. 1 5 b) 8 2 8. -31 -3 7

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Q: -2 - Find the inverse of the matrix A = 6. or state that there is no inverse. 4.

A: A necessary condition for the inverse of a matrix that it must be a non-singular matrix.

Q: 8 Consider a square matrix B whose inverse is given by B'. a In terms of B", what is the inverse of…

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Q: 6 -4 For the matrix A find a matrix C such that C-1AC is in canonical form and 1 state the canonical…

A: Given matrix is A=6−412. We have to find he matrix C such that C−1AC is in canonical form and state…

Q: Find the inverse of the matrix 2 A= 2 -3-3 -31

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Q: 7. (S.15). Find the inverse A-1 of the matrix -2 -3 A = 0 2 -1 -1 -2 3

A: Matrix Question

Q: Q4) For Matrix A = 2 1 2 5 -1 4 1 -1, Find the following: 1 1. The Determinant of A. 2. The Minor of…

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Q: 1 2 Compute the adjoint matrix of A 3 2 2 2 3 Select one: a. -7 4 -5 7 -7 -5 3 -1 -2 %3D -7 -5 41 d.…

A: We have given a matrix and we have to find the adjoint of A.

Q: n 2. Check whether the matrix A- 2 Check whether the matrix A (0 is Hestnitian and Unitary matrix or…

A: The detailed solution is given below Thank you

Q: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1AP =…

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Q: 1 0 2 -2 1 –1 3 find cofactor of matrix .a -5 -3 -6 6. 3 7 -2 -1 -2 .b 6. -6 -3 -7 2 .C -5 -6 -2 3 1…

A: Cofactor of a particular element of in Matrix can be obtained by using the particular sign and…

Q: 3. Find m and n so that the matrix below is symmetric:

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Q: 1. If 1+ A is nonsingular, show that (I+ A)"' and I– A commute and (I + A) +(I+ A')"=1, where I is…

A: Given I+A is nonsingular and we have to show that I+A-1 and I-A commute and  I+A-1+I+A-1-1=I

Q: Q5. Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is…

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Q: Find the inverse of the matrix 2 2 2 -3 -3 !

A: Given  A = 122112-3-31

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: A = 60- -5 1 0 0 9 2 M33 = A33 = 32

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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: 10 0 3. Let A = 3 0 1 0 2 2 (a) (. (b) (. ) Find the cofactor matrix C -) Use the cofactor matrix to…

A: To find  The cofactor matrix and the inverse matrix from the given matrix A

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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