Download App

3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
If $A = \left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right]$and $I = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$, ${A^2} - 6A = $
  • A
    $3I$
  • B
    $5I$
  • ✓
    $-5I$
  • D
    None of these
✓

Answer

Correct option: C.
$-5I$
c
(c) ${A^2} - 6\,A = \left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right] - 6\left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{c}}{19}&6\\{18}&7\end{array}} \right] - \left[ {\begin{array}{*{20}{c}}{24}&6\\{18}&{12}\end{array}} \right]$$\left[ {\begin{array}{*{20}{c}}{ - 5}&0\\0&{ - 5}\end{array}} \right] = - 5I$.

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 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The two parts of  $100 $ for which the sum of double of first and square of second part is minimum, are
→
Let the area of the region $\{(x, y): 0 \leq x \leq 3,0 \leq y \leq$ $\left.\min \left\{x^2+2,2 x+2\right\}\right\}$ be $A$. Then $12 \mathrm{~A}$ is equal to
→
If $f(x) = x, - 1 \le x \le 1$, then function $f(x)$ is
→
$\int_{}^{} {\frac{{x{e^x}}}{{{{(1 + x)}^2}}}dx = } $
→
If $\text{A}=\begin{bmatrix} 2 & -1 \\ 3 & -2 \end{bmatrix},$ then An =

  1. $\text{A}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix},$ if n is an even natural number

  2. $\text{A}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix},$ if n is an odd natural number

  3. $\text{A}=\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix},\text{if n}\in\text{N}$

  4. None of these.

→
A biased coin with probabilty p, 0 < p < 1, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $\frac{2}{5},$ then p equals:
→
The area bounded by a curve, the axis of co-ordinates $\&$ the ordinate of some point of the curve is equal to the length of the corresponding arc of the curve. If the curve passes through the point $P (0, 1)$ then the equation of this curve can be
→
lf $\text{AB}\perp\text{BC}$ then the value of $\lambda$ equal, where A(2k, 2, 3), B(k, 1, 5), C(3 + k, 2, 1):
  1. $3$
  2. $\frac{1}{3}$
  3. $-3$
  4. $-\frac{1}{3}$
→
If the matrix AB is zero, then:
  1. It is not necessary that either A = 0 or, B = 0
  2. A = 0 or B = 0
  3. A = 0 and B = 0
  4. All the above statements are wrong
→
Let $f\left( x \right) = \int\limits_0^x {g\left( t \right)dt} $, where $g$ is a non zero even function. If $f(x+5) = g(x)$ , then $\int\limits_0^x {f\left( t \right)dt} $ equals
→