1. Let A be the matrix given below, in which a and b are real numbers. 0 0 b 0 a a 0 00 a 0 0 0 b 0 A = (a) Find all values of a and b for which A is diagonalizable. (b) For any values for which it is diagonalizable, diagonalize it (meaning find the invertible P and diagonal D such that A = PDP-¹).

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A: The objective of this question is to understand the relationship between the invertibility of a…

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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: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

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Q: Prove that (a) C(B) C Nul(A), where C(B) denotes the column space of B. (b) rank A + rank B < 5

A: Given that A is a 3×5 matrix and B is a 5×6 matrix. Also AB=0.

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A: If A is invertible matrix then it has trivial null space and a matrix is invertible iff AT is…

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Q: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

A: Given: Where, X is a diagonal matrix of A, then 7X is also diagonalizing matrix of A. To determine:…

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Q: 6. Let A be a 2x 2 matrix such that (a) The above equations can be written in the form A -1 0 -1 0 B…

A: The objective is to find the matrix B. heck whether the matrix B is diagonalizable or not and also…

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A: If the equation Ax = 0 has non-trivial solutions, the matrix A is not invertible.Explanation:Steps…

Q: e a square Fits diagona diagonal ele anal the val

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Q: 5 3 [B] -5 -6 i.e. write A = LU where L is a lower triangular matrix with 1's on the diagonal, and U…

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

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A: Consider the given matrix,

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A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…

Q: 6. 1 4 If w = -3 E span 2 then x = 1 4 3 Select one: True 21 False

A: As per guidelines, we will solve only first question. Kindly repost other question separately.