Download App

Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMatrices2 Marks
Question
Find $x$ and $y$, if $2\left[\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right]+\left[\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right]$.
✓

Answer

Given: $2\left[ {\begin{array}{*{20}{c}} 1&3 \\ 0&x \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} y&0 \\ 1&2 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 5&6 \\ 1&8 \end{array}} \right]$
$\Rightarrow \left[ {\begin{array}{*{20}{c}} 2&6 \\ 0&{2x} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} y&0 \\ 1&2 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 5&6 \\ 1&8 \end{array}} \right]$
$\Rightarrow \left[ {\begin{array}{*{20}{c}} {2 + y}&6 \\ 1&{2x + x} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 5&6 \\ 1&8 \end{array}} \right]$
Equating corresponding entries, we have
2 + y = 5 and 2x + 2 = 8
$\Rightarrow$ y = 5 - 2 and 2(x + 1) = 8
$\Rightarrow$ y = 3 and x + 1 = 4
$\Rightarrow$ y = 3 and x = 3

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 "2 Marks Questions" 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

Differentiate $a^x w.r.t. x,$ where a is a positive constant.
→
Evaluate the following integrals:
$\int\bigg\{\text{x}^2+\text{e}^{\log\text{x}}+\Big(\frac{\text{e}}{2}\Big)^\text{x}\bigg\}\text{dx}$
→
Find the equation of the line passing through the points (2, -1, 3) and parallel to the line $\vec{\text{r}}=\big(\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}\big)+\lambda\big(2\hat{\text{i}}+3\hat{\text{j}}-5\hat{\text{k}}\big).$
→
A and B are two events such that P (A) $\ne$ 0. Find P(B|A), if A is a subset of B.
→
Evaluate the following integrals:
$\int\text{x}\text{ cosec}^2\text{x dx}$
→
Prove the following results:
$\tan^{-1}\frac{1}{7}+\tan^{-1}\frac{1}{13}=\tan^{-1}\frac{2}{9}$
→
Determine whether the following operations define a binary operation on the given set or not:
$'+6\ '$ on $S = \{0, 1, 2, 3, 4, 5\} $ defined by, $\text{a}+_6\text{b}=\begin{cases}\text{a}+\text{b},&\text{if a}+\text{b}<6\\\text{a}+\text{b}-6,&\text{if a}+\text{b}\geq6\end{cases}$
→
Prove that the following function are increasing on $R.$
$f(x) = 4x^3 + 18x^2 + 27x - 27$
→
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=2\text{x}^2-5\text{x}+3\text{ on }[1,3]$
→
Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\text{A}\cap\overline{\text{B}})$
→