Download App

Algebra of Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAlgebra of Matrices3 Marks
Question
If $\text{x}\begin{bmatrix}2\\3 \end{bmatrix}+\text{y}\begin{bmatrix}-1\\1 \end{bmatrix}=\begin{bmatrix}10\\5 \end{bmatrix},$ find the value of x.
✓

Answer

$\text{x}\begin{bmatrix}2\\3 \end{bmatrix}+\text{y}\begin{bmatrix}-1\\1 \end{bmatrix}=\begin{bmatrix}10\\5 \end{bmatrix}$
$\Rightarrow\begin{bmatrix}2\text{x}-\text{y}\\3\text{x + y} \end{bmatrix}=\begin{bmatrix}10\\5 \end{bmatrix}$
Corresponding elements of equal matrices are equal.
⇒ 2x - y = 10 and 3x + y = 5
⇒ y = 2x - 10 and 3x + (2x - 10) = 5
⇒ y = 2x - 10 and 5x = 15
⇒ y = 2x - 10 and x = 3
⇒ y = 2(3) - 10 and x = 3
⇒ y = -4 and x = 3
$\therefore$ x = 3 and y = -4
Hence, the value of x is 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 "3 Marks Question" from Algebra of Matrices→Algebra of Matrices — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Cartesian equations of a line AB are $\frac{2\text{x}-1}{2}=\frac{4-\text{y}}{7}=\frac{\text{z}+1}{2}.$ Write the direction ratios of a parallel to AB.
→
Evaluate the following integrals:
$\int\sqrt{16\text{x}^2+25}\text{dx}$
→
Differentiate the function $\sqrt {\frac{{\left( {x - 1} \right)\left( {x - 2} \right)}}{{\left( {x - 3} \right)\left( {x - 4} \right)\left( {x - 5} \right)}}} $ w.r.t. x.
→
Show that the points $A\left( {2\hat i - \hat j + \hat k} \right),B\left( {\hat i - 3\hat j - 5\hat k} \right),C\left( {3\hat i - 4\hat j - 4\hat k} \right)$ are the vertices of a right angled triangle.
→
In the following, determine the values of constants involved in the definition so that the given function is continuous:
$\text{f(x)}=\begin{cases}\text{k}(\text{x}^2+3\text{x}),&\text{if }\text{ x}<0\\\cos2\text{x},&\text{if }\text{ x}\geq0\end{cases}$
→
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
→
Given the matrices
$\text{A}=\begin{bmatrix}2&1&1\\3&-1&0\\0&2&4\end{bmatrix},\text{B}=\begin{bmatrix}9&7&-1\\3&5&4\\2&1&6\end{bmatrix}$ and $\text{C}=\begin{bmatrix}2&-4&3\\1&-1&0\\9&4&5\end{bmatrix}$ Verify that (A + B) + C = A + (B + C).
→
Evalute the following integrals:
$\int\frac{\text{a}}{\text{b}+\text{ce}^\text{x}}\text{dx}$
→
Find the integrals of the functions in Exercises:
$\frac{\sin^2\text{x}}{1+\cos\text{x}}$
→
Write the following function in the simplest form:
$\tan^{-1}\bigg(\frac{3a^{2}x-x^{3}}{a^{3}-3ax^{2}}\bigg), a>0; \frac{-a}{\sqrt{3}}\leq x\leq\frac{a}{\sqrt{3}}$
→