1 -1 1 1 1 3 -1 1 Let, A = -2 1 4 -1 3 3 -1 -5 1 -6 a. Find a 5x5 matrix B such that AB = 0, where 0 is the 4x5 zero matrix b Suppose C is a 5x5 matrix such that AC = 0. Prove that rank(C) < 2.

Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

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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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Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

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Q: 2 -1 3 1 0 0 1 A = -1 2 no

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Q: Diagonalize the matrix 1 0 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix D…

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Q: Let A and B be the matrices as shown. '1 2 1 1 2 1 ^ - ( ²³ ) ·- - 6 ÷ ³) A = 0 5 1 B = 2 -1 4 2 −1…

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Q: Find the LDU factorization of -2 -2 6 4 -15 -10 A = -6 3 -13 -14 -2 14 46 35 That is, write A = LDU…

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Q: Find a 3 x 3 matrix A such that A A A A = 1 4 0 = 2 0 -1 B-B EL. 0 2 1 = -3 and 0 -5 0 -5 B-B 0 -5 1…

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Q: real matrix which is not diagonal. If (A + I)² = 0,

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Q: Let -1 1 A = -1 1 -1 -3 3 Find an upper triangular matrix which is orthogonally similar to A.

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Q: Let A be a 3x6 matrix of rank 3 then nullity of A equal 0 Select one: True False

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