Given-matrix-A-1-0-2-3-B-1-3-2-0-and-AX-2B-I-what-the-value-of-det-X-

Question Number 112505 by bemath last updated on 08/Sep/20

Given matrix A = (\begin{matrix} 1 0 \\ 2 3 \end{matrix}), B = (\begin{matrix} - 1 - 3 \\ 2 0 \end{matrix})

and AX + 2 B = I . what the value

of \det (X) ?

Answered by john santu last updated on 08/Sep/20

\Leftrightarrow A X = (\begin{matrix} 1 0 \\ 0 1 \end{matrix}) - (\begin{matrix} - 2 - 6 \\ 4 0 \end{matrix})

\Leftrightarrow A X = (\begin{matrix} 3 6 \\ - 4 1 \end{matrix}) .

d e t (X) = \frac{| \begin{matrix} 3 6 \\ - 4 1 \end{matrix} |}{| \begin{matrix} 1 0 \\ 2 3 \end{matrix} |} = \frac{27}{3} = 9 .