(24) Let A be the matrix 1 0 0 2 1 0 3 4 1 (a) Following the normal row reduction methodology, find A-¹ keeping track of

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24 Let A Be The Matrix 1 0 0 2 1 0 3 4 1 A Following The Normal Row Reduction Methodology Find A Keeping Track Of 1 (57.15 KiB) Viewed 31 times

(24) Let A be the matrix 1 0 0 2 1 0 3 4 1 (a) Following the normal row reduction methodology, find A-¹ keeping track of the elementary row operations matrices E₁, E2,..., Ek. Write A-¹ as a product of these matrices. i.e. Explicitly write A-¹ in the form A¹ EE₂E₁. = (b) Produce a different elementary matrices factorization by first using row 2 of A to eliminate position (3, 2) and then precede as normal. (c) Recall that the book asserts every invertible matrix can be written as a product of elementary matrices. This is equivalent to saying that all invertible matrices factor over elementary matrices. Considering the prior parts, do you think that the invertible matrices factor uniquely over the elementary matrices?