Download App

Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}4 & 0 \\ -1 & 1\end{array}\right]$, then value of $x$ for which $A^2=B$ is
  • A
    -2
  • B
    2
  • C
    2 or -2
  • D
    1
✓

Answer

Given, $A=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}4 & 0 \\ -1 & 1\end{array}\right]$
Now, $A^2=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]=\left[\begin{array}{cc}x^2 & 0 \\ x+1 & 1\end{array}\right]$
$\begin{array}{c}
A^2=B \\
\Rightarrow\left[\begin{array}{cc}
x^2 & 0 \\
x+1 & 1
\end{array}\right]=\left[\begin{array}{cc}
4 & 0 \\
-1 & 1
\end{array}\right]
\end{array}$
On comparing, we get $x^2=4$ and $x+1=-1$
$\Rightarrow x= \pm 2$ and $x=-2$
$\therefore \quad$ Required value of $x$ is -2 .

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 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

$\int_{}^{} {\frac{1}{{{x^2}}}\log ({x^2} + {a^2})dx = } $
→
If $\triangle_1=\begin{vmatrix}1&1&1\\\text{a}&\text{b}&\text{c}\\\text{a}^2&\text{b}^2&\text{c}^2\end{vmatrix},\triangle_2=\begin{vmatrix}1&\text{bc}&\text{a}\\1&\text{ca}&\text{b}\\1&\text{ab}&\text{c}\end{vmatrix},$ then:
→
If a relation $R$ is defined on $A=\{1,2,3\}$, then $R$ is, where $R =\{(1,1),(2,2),(3,3),(1,2),(2,3)$, $(1,3)\}$ :
→
Suppose the limit  $L=\lim _{n \rightarrow \infty} \sqrt{n} \int_0^1 \frac{1}{\left(1+x^2\right)^n} d x$  exists and is larger than $\frac{1}{2}$. Then,
→
The solution set of the inequation 2x + y > 5 is:
→
If $A = \left[ {\begin{array}{*{20}{c}}a&0&0\\0&b&0\\0&0&c\end{array}} \right]$, then ${A^n} = $
→
If $f(x) = \left\{ \begin{array}{l}{x^2}\sin \frac{1}{x},\;\;\;{\rm{when\,\, }}x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,\,\,\,{\rm{when\,\,}}\,x = 0\end{array} \right.$, then
→
If a matrix has $13$ elements, then the possible dimensions $($orders$)$ of the matrix are:
→
If $R$ is a relation on the set $A = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ given by $xRy \Rightarrow y = 3x,$ then $R =$
→
The value of $\int \sec ^2(2 x+1) d x$ is
→