Download App

Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMatrices2 Marks
Question
Find the values of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and $\mathrm{d}$ from the equation $\left[\begin{array}{cc}a-b & 2 a+c \\ 2 a-b & 3 c+d\end{array}\right]=\left[\begin{array}{cc}-1 & 5 \\ 0 & 13\end{array}\right]$.
✓

Answer

Equating corresponding entries,
a - b = -1 ……….(i)
2a - b = 0 ……….(ii)
2a + c = 5 ……….(iii)
3c + d = 13 ……….(iv)
Eq. (i) – Eq. (ii) = -a = -1
$\Rightarrow$ a = 1
Putting a = 1 in eq. (i), 1 - b = -1
$\Rightarrow$ -b = -2 $\Rightarrow$ b = 2
Putting a = 1 in eq. (iii), 2 + c = 5
$\Rightarrow$ c = 5 - 2 $\Rightarrow$ c = 3
Putting c = 3 in eq. (iv), 9 + d = 13
$\Rightarrow$ d = 13 - 9 $\Rightarrow$ d = 4
$\Rightarrow$ a = 1, b = 2, c = 3, d = 4

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

If the probability distribution of a random variable $X$ is given below:
$X = X_i$ $1$ $2$ $3$ $4$
$P(X = X_i)$ $c$ $2c$ $4c$ $4c$
Write the value of $\text{P}(\text{X}\leq2)$
→
Form the differential equation representing the family of curves $y = e^{2x}(a + bx),$ where $‘a’$ and $‘b’$ are arbitrary constants.
→
Find an anti derivative $($or integral$)$ of function by the method of inspection $(ax + b)^2$
→
Find the second-order derivatives of the function $x^{20}$
→
Write the position vector of a point dividing the line segment joining points having position vectors $\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$ externally in the ratio 2 : 3.
→
Projections of a line on $x, y, z$ axes are respectively 12,5 and $2 \sqrt{14}$. Find the length of the line segment and its direction cosines.
→
The side of a square is increasing at the rate of 0.1cm/ sec. Find the rate of increase of its perimeter.
→
For what value of $\lambda$ are the vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ perpendicular to each other if 
$\vec{\text{a}}=\lambda\hat{\text{i}}+2\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=4\hat{\text{i}}-9\hat{\text{j}}+2\hat{\text{k}}$
→
Evaluate the following integrals:
$\int\bigg (2^{\text{x}}+\frac{5}{\text{x}}-\frac{1}{\text{x}^{\frac{1}{3}}}\bigg)\text{dx}$
→
If $\text{f(x)}=\begin{cases}\frac{\sin^{-1}\text{x}}{\text{x}},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ is continuous at x = 0, write the value of k. 
→