Question
Evaluate $\begin{vmatrix}2&3&-5\\7&1&-2\\-3&4&1\end{vmatrix}$ by two methods.
$|\text{A}|=2\begin{vmatrix}1&-2\\4&1 \end{vmatrix}-3\begin{vmatrix}7&-2\\-3&1\end{vmatrix}-3\begin{vmatrix}7&1\\-3&4\end{vmatrix}$
$=2(1+8)-7(3+20)-3(-6+5)$
$=18-7(23)-3(-1)$
$=21-161$
$=-140$
$|\text{A}|=\begin{vmatrix}1&-2\\4&1 \end{vmatrix}-7\begin{vmatrix}3&-5\\4&1\end{vmatrix}-3\begin{vmatrix}3&-5\\1&-2\end{vmatrix}$
$=2(1+8)-7(3+20)-3(-6+5)$
$=18-7(23)-3(-1)$
$=18-161+3$
$=21-161$
$=-140$
We can see, the answer is same with both the methods.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\int(\text{x}+1)\text{e}^{\text{x}}\log(\text{xe}^{\text{x}})\text{dx}$
$\begin{bmatrix} 1 & 1 & 2 \\ 3 & 1 & 1 \\ 2 & 3 & 1 \end{bmatrix}$
| $\text{X}$ | $0$ | $1$ | $2$ | $3$ |
| $\text{P}(\text{X})$ | $\text{k}$ | $\frac{\text{k}}{2}$ | $\frac{\text{k}}{4}$ | $\frac{\text{k}}{8}$ |