Let A be the matrix A = Z 3 2 X 1 3 2 Y 5...

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Let A be the matrix A = Z 3 2 X 1 3 2 Y 5 where x, y, and z are variables. (a) Compute the adjoint matrix of A (this will still involve the variables x, y, and z). (b) Compute the product of the adjoint matrix and A. (c) Compute det (A). (d) Assuming that det(A) = 0, write down the inverse of A (this will still be a matrix involving x, y, and z). (e) To show that this method really gives a "universal formula for the inverse", plug in the values (x, y, z) = (3,−1, 1) into both A and the inverse matrix from part (d), and multiply them to see that it really gives the inverse for A. (f) Do the same for (x, y, z) = (1, 1, 1) Let A be the matrix A = Z 3 2 X 1 3 2 Y 5 where x, y, and z are variables. (a) Compute the adjoint matrix of A (this will still involve the variables x, y, and z). (b) Compute the product of the adjoint matrix and A. (c) Compute det (A). (d) Assuming that det(A) = 0, write down the inverse of A (this will still be a matrix involving x, y, and z). (e) To show that this method really gives a "universal formula for the inverse", plug in the values (x, y, z) = (3,−1, 1) into both A and the inverse matrix from part (d), and multiply them to see that it really gives the inverse for A. (f) Do the same for (x, y, z) = (1, 1, 1)