Question

Matrix $A = \begin{bmatrix}1&2&3\\\ 1&1&5\\\ 2&4&7\end{bmatrix}$then the value of $a_{31} A_{31} + a_{32} A_{32} + a_{33 } + A_{33}$ is

• A. 1
• B. 13
• C. -1
• D. -13

Answer 1

Answer: (C)

-1

Answer 2

We have, $A = \begin{bmatrix}1&2&3\\\ 1&1&5\\\ 2&4&7\end{bmatrix}$ $a_{31} =2, a_{32} = 4, a_{33} = 7$and $A_{31}=\begin{vmatrix}2&3\\\ 1&5\end{vmatrix}$ $= 10 - 3 = 7$ $A_{32} = -\begin{vmatrix}1&3\\\ 1&5\end{vmatrix}$ $= -\left(5 - 3\right) = -2$ $A_{33} =\begin{vmatrix}1&2\\\ 1&1\end{vmatrix}$ $= 1 - 2 = -1$ $\therefore a_{31} A_{31} + a_{32}A_{32} + a_{33} A_{33}$ $= 2(7) + 4(-2) + 7(-1)$ $= 14 - 8 - 7 = -1$