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 $A = \left[ {\begin{array}{*{20}{c}}1&a\\0&1\end{array}} \right]$, then ${A^4}$ is equal to
  • A
    $\left[ {\begin{array}{*{20}{c}}1&{{a^4}}\\0&1\end{array}} \right]$
  • B
    $\left[ {\begin{array}{*{20}{c}}4&{4a}\\0&4\end{array}} \right]$
  • C
    $\left[ {\begin{array}{*{20}{c}}4&{{a^4}}\\0&4\end{array}} \right]$
  • ✓
    $\left[ {\begin{array}{*{20}{c}}1&{4a}\\0&1\end{array}} \right]$
✓

Answer

Correct option: D.
$\left[ {\begin{array}{*{20}{c}}1&{4a}\\0&1\end{array}} \right]$
d
(d) ${A^2} = A.\,A = \left[ {\begin{array}{*{20}{c}}1&a\\0&1\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&a\\0&1\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&{2a}\\0&1\end{array}} \right]$

${A^3} = A.\,{A^2} = \left[ {\begin{array}{*{20}{c}}1&a\\0&1\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&{2a}\\0&1\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&{3a}\\0&1\end{array}} \right]$

${A^4} = A.\,{A^3} = \left[ {\begin{array}{*{20}{c}}1&a\\0&1\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&{3a}\\0&1\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&{4a}\\0&1\end{array}} \right]$.

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

If $x$ denotes the number of sixes in four consecutive throws of a dice, then $P\,(x = 4)$ is
→
If $\text{y}=\text{a}\sin\text{mx}+\text{b}\cos\text{mx},$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2}$ is equal to:
  1. -m2y
  2. m2y
  3. -my
  4. my
→
Solution of differential equation $\frac{{dy}}{{dx}} + ay = {e^{mx}}$ is
→
If six cards are selected at random (without replacement) from a standard deck of 52 cards, what is the probability that there will be no pairs? (two cards of same denomination)
→
Let $D_1 =$ $\left| {\,\begin{array}{*{20}{c}}a&b&{a + b}\\c&d&{c + d}\\a&b&{a - b}\end{array}\,} \right|$ and $D_2 =$ $\left| {\,\begin{array}{*{20}{c}}a&c&{a + c}\\b&d&{b + d}\\a&c&{a + b + c}\end{array}\,} \right|$ then the value of $\frac{{{D_1}}}{{{D_2}}}$ where $b \ne 0$ and $ad \ne bc$, is
→
Suppose that $g(x) = 1 + \sqrt x $ and $f(g(x)) = 3 + 2\sqrt x + x$, then $f(x)$ is
→
Let $f: R \rightarrow R$ be a function defined by $f(x)=\left(2\left(1-\frac{x^{25}}{2}\right)\left(2+x^{25}\right)\right)^{\frac{1}{50}}$. If the function $g(x)=f(f(f(x)))+f(f(x))$, the the greatest integer less than or equal to $g (1)$ is
→
Any tangent to the curve y = 2x7 + 3x + 5:
  1. Is parallel to x-axis.
  2. Is parallel to y-axis.
  3. Makes an acute angle with x-axis.
  4. Makes an obtuse angle with x-axis.
→
Which of the following differential equations has $\text{y} = \text{c}_1\text{e}^\text{x} + \text{c}_2\text{e}^{-\text{x}}$ as the general solution?
  1. $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{y}=0$
  2. $\frac{\text{d}^2\text{y}}{\text{dx}^2}-\text{y}=0$
  3. $\frac{\text{d}^2\text{y}}{\text{dx}^2}+1=0$
  4. $\frac{\text{d}^2\text{y}}{\text{dx}^2}-1=0$
→
The area enclosed by the curves $y=\sin x+\cos x$ and $y=|\cos x-\sin x|$ over the interval $\left[0, \frac{\pi}{2}\right]$ is
→