Consider matrix 1 3 A =0 -2 0 -2) 1 -1 3 and vectors x = and y =0 Let w = Ax. Evaluate the scalar product of y and w. (Hint: Use the Gauss- Jordan algorithm to find the inverse A- of the matrix A first)

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Q: 1. Let V be the set of all 2 x 2 matrices A = " such that the product abcd=0 with standard…

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Q: Let A and B be nxn inversible matrix. Prove that AB is invertible and (AB)-1=  B-1A-1.

A: Let A and B be n x n invertible matrices, with inverses A-1 and B-1, respectively.

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Q: Assume the invertible matrix A satisfies 10 4 1 1 A 6 A 1 A 1 3 4 -1 -1 -1 1 1 5 -2 1 1 3 4 -3 -1 1…

A: Detailed explanation mentioned below

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A: Note that--- If determinant of a matrix is non-zero then the matrix is said to be invertible and if…

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Q: Determine the Householder matrix that annihilates all but the first entry of the vector v = [2 22…

A: Let α=2222T Then take, v=α-αc1=2222-α2000=2222-α000 ,Here α=±||a||2=±2 Now , since,α1  is positive ,…

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A: GivenA=242501b=12-2TTo find the orthogonal projection of matrix b onto the column space matrix A

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Q: such that the vector 2 is a solution of 13. Construct a 3 x 3 nonzero matrix Ax = 0 123

A: I have construct a block matrix

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A: Now transpose of this matrix is,

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Q: 1. Let V be the set of all 2 x 2 matrices 4- such that the product abcd =0 with standard operations…

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Q: (6) Consider the real symmetric matrix (2 1 0 A = 1 1 2 Construct an orthogonal matrix Q of eigen…

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Q: . Matrix A=(a)nxn is called strictly diagonally dominant, if |au|> Σ |a₁|, i=1,2,...,n. j=1, j*i…

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Q: Given the matrix 6 0 0 A= 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ"

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Q: Which of the following is true or false? a)An orthogonal and symmetric matrix Q satisfies Q2=I…

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