If A= 0&0 4&0 , find A^ 16 . - Vidyadip

Question

If $\text{A}=\begin{bmatrix}0&0\\4&0\end{bmatrix},$ find $A^{16}$.

✓

Answer

Given,
$\text{A}=\begin{bmatrix}0&0\\4&0\end{bmatrix}$
$ \text{A}^2=\text{A}\times\text{A}$
$ =\begin{bmatrix}0&0\\4&0\end{bmatrix}\begin{bmatrix}0&0\\4&0\end{bmatrix}$
$ =\begin{bmatrix}0+0&0+0\\0+0&0+0\end{bmatrix}$
$=\begin{bmatrix}0&0\\0&0\end{bmatrix}$
$=0$
$ \text{A}^4=\text{A}^2\times\text{A}^2$
$=0\times0$
$=0$
$ \text{A}^{16}=\text{A}^4\times\text{A}^4$
$=0\times0$
$=0$
So,
$A^{16}$ is a null matrix

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 "5 Marks Questions" from MATRICES→MATRICES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Discuss the continuity of the following functions at the indicated point:
$\text{f}\text{(x)}=\begin{cases}\frac{2\text{x}+\text{x}^2}{\text{x}}, & \text{x} \neq0\\0,&\text{ x} = 0\end{cases}\text{at x}=0$

If $\text{y}\sqrt{1-\text{x}^2}+\text{x}\sqrt{1-\text{y}^2}=1,$ prove that $\frac{\text{dy}}{\text{dx}}=-\sqrt{\frac{1-\text{y}^2}{1-\text{x}^2}}$

Differentiate the following functions with respect to x:
$\frac{3\text{x}^2\sin\text{x}}{\sqrt{7-\text{x}^2}}$

Find $\frac{\text{dy}}{\text{dx}},$ if $\text{y}=\text{x}^{\tan\text{x}}+\sqrt{\frac{\text{x}^2+1}{2}}.$

Evaluate the following integrals:
$\int\limits_{0}^{\pi}\frac{\sin\text{x}}{\sin\text{x}+\cos\text{x}}\text{ dx}$

By computing the shortest distance determine whether the following pairs of lines intersect or not:
$\vec{\text{r}}=\big(\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}\big)+\lambda\big(3\hat{\text{i}}-\hat{\text{j}}\big)$ and $\vec{\text{r}}=\big(4\hat{\text{i}}-\hat{\text{k}}\big)+\mu\big(2\hat{\text{i}}+3\hat{\text{k}}\big)$

Find the equation of a plane passing through the points (0, 0, 0) and (3, -1,2) and parallel to the line $\frac{\text{x}-4}{1}=\frac{\text{y}+3}{-4}=\frac{\text{z}+1}{7}$

Show that the binary operation $\ast \text{ on A = R - {-1}}$ defined as a $\text{a} \ast \text{b} = \text{a + b + ab}$ for all $\text{a, b}\in \text{A}$ is communicative and associative on A. Also find the identity element of $\ast$ in A and prove that every element of a is invertible.

Differentiate the following functions with respect to x:
$\log(3\text{x}+2)-\text{x}^2\log(2\text{x}-1)$

Show that the surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.