Find the matrix A such that 4 1 3 A= -4&8&4 -1&2&1 -3&6&3 - Vidyadip

Question

Find the matrix A such that
$ \begin{bmatrix}4\\1\\3\end{bmatrix}\text{A}=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$

✓

Answer

Let $\text{A}=\begin{bmatrix}\text{x}&\text{y}&\text{z}\end{bmatrix}$
$\Rightarrow\begin{bmatrix}4\\1\\3\end{bmatrix}\begin{bmatrix}\text{x}&\text{y}&\text{z}\end{bmatrix}=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$
$\Rightarrow\begin{bmatrix}4\text{x}&4\text{y}&4\text{z}\\\text{x}&\text{y}&\text{z}\\3\text{x}&3\text{y}&3\text{z}\end{bmatrix}=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$
The corresponding elements of two equal matrices are equal.
⇒ 4x = -4 ...(1)
4y = 8 ...(2)
4z = 4 ...(3)
⇒ x = -1, y = 2 and z = 1
$\therefore\ \text{A}=\begin{bmatrix}-1&2&1\end{bmatrix}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from MATRICES→MATRICES — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the distance of the point $2\hat{\text{i}}-\hat{\text{j}}-4\hat{\text{k}}$ from the plane $\vec{\text{r}}\cdot(3\hat{\text{i}}-4\hat{\text{j}}+12\hat{\text{k}})-9=0$

Solve the following differential equation:$\frac{dy}{dx} + 2y = \text6 {e^{x}}$

Prove that the function $f : N \rightarrow N,$ defined by $f(x) = x^2 + x + 1$ is one$-$one but not onto. Find inverse of $f : N \rightarrow S,$ where $S$ is range of $f.$

Evaluate the following definite integrals:
$\int_{0}^\limits{1}\Big(\text{xe}^{2\text{x}}+\sin\frac{\pi\text{x}}{2}\Big)\text{dx}$

Differentiate $\log(1+\text{x}^2)$ with respect to $\tan^{-1}\text{x}$

Evalute the following integrals:
$\int\frac{\cos\text{x}}{\cos(\text{x}-\text{a})}\text{dx}$

If the matric $\text{A}=\begin{bmatrix}5 & 2&\text{x} \\\text{y} & \text{z}&-3\\4&\text{t}&-7\end{bmatrix}$ is a symmetric matrix, find $x, y, z$ and $t.$

Find the mean and standard deviation of the following probability distributions:

$x_i$	$1$	$2$	$3$	$4$
$p_i$	$0.4$	$0.1$	$0.2$	$0.3$

Evalute the following integrals:
$\int\frac{\sin2\text{x}}{\sin5\text{x}\sin3\text{x}}\text{dx}$

Write the minors and cofactors of element of the first column of the following matrices and hence evaluate the determinant in case:
$\text{A}=\begin{vmatrix}5&20\\0&-1 \end{vmatrix}$