Download App

STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
If $A = \left[ {\begin{array}{*{20}{c}}
3&7\\
1&2
\end{array}} \right]$ then $|A^{2011} -5A^{2010}|$ is equal to
  • A
    $1$
  • ✓
    $-1$
  • C
    $6$
  • D
    $-6$
✓

Answer

Correct option: B.
$-1$
b
$\left|\mathrm{A}^{2011}-5 \mathrm{A}^{2010}\right|=|\mathrm{A}|^{2010}|\mathrm{A}-5 \mathrm{I}|$

$A-5 I=\left(\begin{array}{ll}{3} & {7} \\ {1} & {2}\end{array}\right)-\left(\begin{array}{ll}{5} & {0} \\ {0} & {5}\end{array}\right)=\left(\begin{array}{cc}{-2} & {7} \\ {1} & {-3}\end{array}\right)$

$|A-5 I|=-1$ and $|A|=-1$

So $|\mathrm{A}|^{2010}|\mathrm{A}-5 \mathrm{I}|=(-1)^{2010}(-1)=-1$

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 "M.C.Q (1 Marks)" from STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int_{}^{} {\frac{{x - 1}}{{{{(x + 1)}^3}}}{e^x}\;dx = } $
→
Let $\overrightarrow{ a }=2 \hat{ i }-3 \hat{ j }+4 \hat{ k }$ and $\overrightarrow{ b }=7 \hat{ i }+\hat{ j }-6 \hat{ k }$ If $\overrightarrow{ r } \times \overrightarrow{ a }=\overrightarrow{ r } \times \overrightarrow{ b }, \overrightarrow{ r } \cdot(\hat{ i }+2 \hat{ j }+\hat{ k })=-3,$ then $\overrightarrow{ r } \cdot(2 \hat{ i }-3 \hat{ j }+\hat{ k })$ is equal to
→
If $y = {1 \over 4}{u^4},u = {2 \over 3}{x^3} + 5$, then ${{dy} \over {dx}} = $
→
From a lot of $10$ items, which include $3$ defective items, a sample of $5$ items is drawn at random. Let the random variable $\mathrm{X}$ denote the number of defective items in the sample. If the variance of $X$ is $\sigma^2$, then $96 \sigma^2$ is equal to....................
→
For the $LP$ problem

Minimize $z=2 x+3 y$ the coordinates of the corner points of the bounded feasible region are $A\,(3,3), B\,(20,3),$ $\mathrm{C}\,(20,10), \mathrm{D}\,(18,12)$ and $\mathrm{E}\,(12,12) .$ The minimum value of $z$ is $\ldots \ldots$

→
If ${x^x}{y^y}{z^z} = c$, then ${{\partial z} \over {\partial x}} = $
→
If $u = {x^2}{\tan ^{ - 1}}{y \over x} - {y^2}{\tan ^{ - 1}}{x \over y}$, then ${{{\partial ^2}u} \over {\partial x\,\partial \,y}} = $
→
If $\log _e\left(1+\frac{d^2 y}{d x^2}\right)=x$, then find the sum of order and degree of given differential equation.
→
$\cos[\tan^{-1}\{\sin(\cot^{-1}\text{x})\}]$ is equal to:
→
If an error of $k\ %$ is made in measuring the radius of a sphere, then percentage error in its volume is:
→