# Math Help - matrices-solution

1. ## matrices-solution

Hi, can anyone help me solve this question?

Which of the matrices are solution of A²-14A=-48I?

a) {{-1,1/a},{a,-1}};
b) {{14,1/a},{a,14}};
c) {{7,1/a},{a,7}};
d) {{7,a},{1/a,-48}};
e) {{-48,0},{0,-48}};

I replaced the "A" for each of the matrices, but nothing

2. ## Re: matrices-solution

Originally Posted by NLG
a) {{-1,1/a},{a,-1}}; b) {{14,1/a},{a,14}}; c) {{7,1/a},{a,7}}; d) {{7,a},{1/a,-48}}; e) {{-48,0},{0,-48}};
For the matrix in c):

$A^2-14A=\begin{bmatrix}{50}&{14/a}\\{14a}&{50}\end{bmatrix}-14\begin{bmatrix}{7}&{1/a}\\{a}&{7}\end{bmatrix}=-48\begin{bmatrix}{1}& 0\\{0}&{1} \end{bmatrix}=-48I$

P.S. If you have covered some properties about trace and determinant, then you could reason that the only possible solution is c).

3. ## Re: matrices-solution

all right, easy question. Thanks