Download App

Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMatrices1 Mark
Question
If $A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], B=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]$ and $A=B^2$, then $x$ equals
✓

Answer

Wehave, $A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]$
$\therefore B^2=\left[\begin{array}{ll}
x & 0 \\
1 & 1
\end{array}\right]\left[\begin{array}{ll}
x & 0 \\
1 & 1
\end{array}\right]=\left[\begin{array}{cc}
x^2 & 0 \\
x+1 & 1
\end{array}\right]$
Now, it is given that $A=B^2$
$\Rightarrow\left[\begin{array}{ll}
1 & 0 \\
2 & 1
\end{array}\right]=\left[\begin{array}{cc}
x^2 & 0 \\
x+1 & 1
\end{array}\right]$
On comparing, we get
$\begin{array}{ll} 
& x^2=1 \text { and } x+1=2 \Rightarrow x= \pm 1 \text { and } x=1 \\
\therefore & x=1
\end{array}$

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $A$ and $B$ are $2 \times 2$ matrices, then which of the following is true?
→
The value of $\int\frac{\sin\text{x}+\cos\text{x}}{\sqrt{1-\sin2\text{x}}}\text{ dx}$ is equal to:
  1. $\sqrt{\sin2\text{x}}+\text{C}$
  2. $\sqrt{\cos2\text{x}}+\text{C}$
  3. $\pm(\sin\text{x}-\cos\text{x})+\text{C}$
  4. $\pm\log(\sin\text{x}-\cos\text{x})+\text{C}$
→
If P(x, y, z) moves such that x = 0, z = 0 then the locus of P is the line whose d.cs are:
→
Which of the following is correct:
  1. Determinant is a square matrix
  2. Determinant is a number associated to a matrix
  3. Determinant is a number associated to a square matrix
  4. None of these
→
Choose the correct answer: Smaller area enclosed by the circle $x^2 + y^2 = 4$ and the line $x + y = 2$ is:
→
vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are inclined at angle $\theta=120^\circ.$ if $|\vec{\text{a}}|=1,\big|\vec{\text{b}}\big|=2,$ then $\big[\big(\vec{\text{a}}+3\vec{\text{b}}\big)\times\big(3\vec{\text{a}}-\vec{\text{b}}\big)\big]^2$ is equal to:
  1. 300
  2. 325
  3. 275
  4. 225
→
Three persons, A, B and C fine a target in turn starting with A. Their probability of hitting the target are 0.4, 0.2 and 0.2, respectively. The probability of two hits is
  1. 0.024
  2. 0.452
  3. 0.336
  4. 0.188
→
If $P(A)=\frac{3}{10}, P(B)=\frac{2}{5}$ and $P(A \cup B)=\frac{3}{5}$, then $P(B \mid A)+P(A \mid B)$ equals
→
Let the differential equation is $\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}=\frac{d^2 y}{d x^2}$. Which of the following statements is/are true?
(i) Degree of the differential equation is 2 .
(ii) Order of the differential equation is 3 .
(iii) Order and degree of differential equation respectively are 2,2 .
→
If matrix $\text{A}=\big[\text{a}_{\text{ij}}\big]_{2\times2'}$ where $\text{a}_\text{ij}=\begin{cases}1,&\text{if }\text{i }\neq\text{j}\\0,&\text{if }\text{i }=\text{j}\end{cases},$ then $A^2$ is equal to$:$
→