Let A R4, 4 be a matrix that can be decomposed as A = P D P-1 , with matrix P an

Question

Let A R4, 4 be a matrix that can be decomposed as A = P D P-1 , with matrix P an invertible matrix and the matrix D = diag(2, 1/4, 2, 3). Knowing only this information about the matrix A. is it possible to compute the det(A)? If your answer is no, explain why not; if your answer is yes, compute det(A) and show your work. Let A R4, 4 be a matrix that can be decomposed as A = P D P-1 , with matrix P an invertible matrix and the matrix D = diag(2, 0, 2, 5). Knowing only this information about the matrix A, is it possible to whether A invertible? Is it possible to know tr (A)? If your answer is no, explain why not; if your answer is yes, compute tr (A) and show your work.

Explanation / Answer

A. yes A=PDP-1 |A|=|PDP-1| =|P|*|D|*|P-1| =|D| =2*(1/4)*2*3 =3 B. yes A=PDP-1 |A|=|PDP-1| =|P|*|D|*|P-1| =|D| =2*0*2*5 =0

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