Compute indicated products left[begin{array}{ccc}3 & -1 & 3 -1 & 0 & 2end{arra

English

Gujarati

Hindi

3 and 4 .Determinants and Matrices

easy

Compute the indicated products $\left[\begin{array}{ccc}3 & -1 & 3 \\ -1 & 0 & 2\end{array}\right]\left[\begin{array}{cc}2 & -3 \\ 1 & 0 \\ 3 & 1\end{array}\right]$

A

$\left[\begin{array}{cc}14 & -6 \\ 4 & 5\end{array}\right]$

B

$\left[\begin{array}{cc}14 & -6 \\ 4 & 5\end{array}\right]$

C

$\left[\begin{array}{cc}14 & -6 \\ 4 & 5\end{array}\right]$

D

$\left[\begin{array}{cc}14 & -6 \\ 4 & 5\end{array}\right]$

Solution

$\left[\begin{array}{ccc}3 & -1 & 3 \\ -1 & 0 & 2\end{array}\right]\left[\begin{array}{cc}2 & -3 \\ 1 & 0 \\ 3 & 1\end{array}\right]$

$=\left[\begin{array}{cc}3(2)-1(1)+3(3) & 3(-3)-1(0)+3(1) \\ -1(2)+0(1)+2(3) & -1(-3)+0(0)+2(1)\end{array}\right]$

$=\left[\begin{array}{cc}6-1+9 & -9-0+3 \\ -2+0+6 & 3+0+2\end{array}\right]=\left[\begin{array}{cc}14 & -6 \\ 4 & 5\end{array}\right]$

Standard 12

Mathematics

Share

Similar Questions

Construct a $2 \times 2$ matrix, $A=\left[a_{ij}\right]$, whose elements are given by : $a_{i j}=\frac{(i+j)^{2}}{2}$

medium

Let $A=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]$. If the sum of the diagonal elements of $\mathrm{A}^{13}$ is $3^{\mathrm{n}}$, then $\mathrm{n}$ is equal to ……….

hard

(JEE MAIN-2024)

If $A$ and $B$ are square matrices of same order, then

normal

Let $M$ be a $3 \times 3$ matrix satisfying $M\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{c}-1 \\ 2 \\ 3\end{array}\right], \quad M\left[\begin{array}{c}1 \\ -1 \\ 0\end{array}\right]=\left[\begin{array}{c}1 \\ 1 \\ -1\end{array}\right]$, and $M\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=\left[\begin{array}{c}0 \\ 0 \\ 12\end{array}\right]$ Then the sum of the diagonal entries of $M$ is

hard

(IIT-2011)

If the matrix $A=\left(\begin{array}{cc}0 & 2 \\ K & -1\end{array}\right)$ satisfies $A\left(A^{3}+3 I\right)=2 I$ then the value of $\mathrm{K}$ is :

hard

(JEE MAIN-2021)