Select all of the following matrices that are diagonal matrices. 1 0 0 0 0-1 0 0 0 2 0 0 0 0 0 3 0 0 4 02 0 0 0 0 1 0 000 0 1 0 00 0 1 0 0 001 0 000 1 000 01 0 0 0 0 0 0 0 0 00 0 0 0 0 0 1 001 0

Q: Find the inverse of this matrix

A: We will use the formula  With a=3, b=1, c=5, d=2

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

Q: and the SUD of the following am A= 11 94040 220

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Q: 1 2 A= -2 4 -2 4 3 5 -1 5 4 3 3 7 6 6

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Q: Let B be an n × m matrix whose columns are linearly independent. Show that B has a left inverse.

A: Let B be an n × m matrix whose columns are linearly independent. To Show:  B has a left inverse.

Q: Let A and B be similar matrices Show that if A? = A then B = B.

A: Two matrices C and D are said to be similar matrices if there exists a non-singular matrix P such…

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Q: 2. Calculate the following matrix products: 1 -1 -1 3. A.

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Q: Let A and B be n x n invertible matrices. Use matrix algebra to simplify A(A¯¹ + B¯¹)B.

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Q: Find a 3 x 3 matrix satisfying the following properties: • A has two eigenvalues: X₁ 2 The vectors…

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

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Q: ) Write the following matrix as a product of elementary matrices: H 1 1 0 02 -3 1

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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: Consider the following matrices: 4 4-[ A = 1 Find a matrix B such that and a matrix C such that 5 4…

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Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

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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