Find the value of x, if 3x+y&-y 2y-x&3 = 1&2 -5&3 - Vidyadip

Question

Find the value of x, if $\begin{bmatrix}3\text{x+y}&-\text{y}\\2\text{y}-\text{x}&3 \end{bmatrix}=\begin{bmatrix}1&2\\-5&3 \end{bmatrix}$

✓

Answer

The corresponding elements of two equal matrices are equal. Given: $\begin{bmatrix}3\text{x+y}&-\text{y}\\2\text{y}-\text{x}&3 \end{bmatrix}=\begin{bmatrix}1&2\\-5&3 \end{bmatrix}$ 3x + y = 1 ...(1) -y = 2 ⇒ y = -2Putting the value of y in eq. (1)
3x + (-2) = 1 ⇒ 3x -2 = 1 ⇒ 3x = 1 + 2 ⇒ 3x = 3 $\Rightarrow\text{x}=\frac{3}{3}=1$ $\therefore $ x = 1

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 Algebra of Matrices→Algebra of Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

For the principal values of the following:
$\cot^{-1}\Big(-\sqrt3\Big)$

The probability distribution of random variable X is given below:

$\text{X}$	$0$	$1$	$2$	$3$
$\text{P}(\text{X})$	$\text{k}$	$\frac{\text{k}}{2}$	$\frac{\text{k}}{4}$	$\frac{\text{k}}{8}$

Determine $\text{P}(\text{X}\leq2)$ and $\text{P}(\text{X}>2)$

Determine whether or not the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation give justification of this.
On $R$, define $*$ by $a * b = a + 4b^2$
Here, $Z^+$ denotes the set of all non-negative integers.

Find the second order derivatives of the function given in Exercise:
$\log(\log\text{x})$

Define direction cosines of a direction line.

Write the value of $\sin^{-1}\Big(\frac{1}{3}\Big)-\cos^{-1}\Big(-\frac{1}{3}\Big).$

Evaluate: $\int \sec ^{\frac{4}{3}} x \csc ^{\frac{8}{3}} x d x$

Write the value of $\cos\big(\sin^{-1}\text{x}+\cos^{-1}\text{x}\big),|\text{x}|\leq1$

Construct a $2 \times 3$ matrix $A = [a_{ij}]$ whose elements $a_{ij}$ are give by:
$a_{ij} = i.j$

Find $\frac{{dy}}{{dx}},$ $y = {\sin ^{ - 1}}\left( {\frac{{1 - {x^2}}}{{1 + {x^2}}}} \right),0 < x < 1$