Question:

5. Given the following matrices 1 2 5 -1 1 -4 A= -1 4 -3 1 -4 7 1 2

5. Given the following matrices
                 1       2       5
               -1       1      -4
        A=   -1      4      -3
                 1     -4       7   
                 1       2       1

(a) Find an orthogonal basis for the column space of each matrix A
(b) Find a QR factorization of the matrix A
(c) Decompose matrix A into its component matrices such that A=UΣVᵗ

5. Given the following matrices 1 2 5 -1 1 -4 A= -1 4 -3 1 -4 7 1 2 1 (a) Find an orthogonal basis for the column space of each matrix A (b) Find a QR factorization of the matrix A (c) Decompose matrix A into its component matrices such that A=UΣVᵗ