Given the following matrix: A = [a b c d e f g h i] (a) Show the product AI axin

Question

Given the following matrix: A = [a b c d e f g h i] (a) Show the product AI axing (columns of A) times (raws of I). (b) Suppose you solve Ax = b for three special right-sides b: Ax_1 = [1 0 0] Ax_2 = [0 1 0] Ax_3 = [0 0 1] If the three solutions x_1, x_2, x_3 are the columns of a matrix X (i. E. X = [x_1 x_2 x_3]), what is the product AX? (c) If the three solutions in part (b) are x_1 = [1 1 1]^T, x_2 = [0 1 1]^T, x_2 = [0 1 1]^T, x_3 = [0 0 1]^T: (i) Determine A^-1. (ii) A^-1 is triangular, (fill in the blank) (iii) Solve Ax = b when b = [3 5 8]^T. (iv) Determine A. You may not use an inverse formula or Gauss-Jordan Elimination. (v) A is triangular, (fill in the blank) (I pt)

Explanation / Answer

a) it gives the answer same as the A only because multiplication with identity will result in A only

b) the combination of Ax1, Ax2, Ax3 gives an idintity matrix so the result is same as above.

C)

i) here A-1 is upper triangular

ii)A is lower triangular

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