Download App

MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES5 Marks
Question
Find matrix A such that
$\begin{pmatrix} 2 & -1 \\ 1 & 0 \\ -3 & 4 \end{pmatrix}\text{A} = \begin{pmatrix} -1 & -8 \\ 1 & -2 \\ 9 & 22 \end{pmatrix}$
✓

Answer

$\text{Let} \begin{pmatrix} 2 & -1 \\ 1 & 0 \\ -3 & 4 \end{pmatrix}\begin{pmatrix} \text{a} & \text{b} \\ \text{c} & \text{d} \end{pmatrix} = \begin{pmatrix} -1 & -8 \\ 1 & -2 \\ 9 & 22 \end{pmatrix}$
$\Rightarrow \begin{pmatrix} \text{2a - c} & \text{2b - d} \\ \text{a} & \text{b} \\ \text{-3a + 4c} & \text{-3b + 4d} \end{pmatrix} = \begin{pmatrix} -1 & -8 \\ 1 & -2 \\ 9 & 22 \end{pmatrix}$
$\Rightarrow $ 2a – c = –1, 2b – d = –8
a = 1, b = –2
–3a + 4c = 9, –3b + 4d = 22
Solving to get a = 1, b = –2, c = 3, d = 4
$\therefore \text{A} = \begin{pmatrix} 1 & -2 \\ 3 & 4 \\ \end{pmatrix}$

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 "5 Marks Questions" from MATRICES→MATRICES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The function $\text{f(x)}=\begin{cases}\frac{\text{x}^2}{\text{a}},&\text{if }0\leq\text{ x}<1\\\text{a},&\text{if }1\leq\text{x}<\sqrt{2}\\\frac{2\text{b}^2-4\text{b}}{\text{x}^2},&\text{if }\sqrt{2}\leq\text{x}<\infty\end{cases}$ is continuous on $(0,\infty),$ then find the most suitable value of a and b.
→
Integrate the function: $\frac{x-1}{\sqrt{x^{2}-1}}$
→
Evaluate the following integrals:
$\int_{0}^\limits{{2\pi}}\sqrt{1-\sin\frac{\text{x}}{2}}\text{ dx}$
→
The volume of a cube increases at a constant rate. Prove that the increase in its surface area varies inversely as the length of the side.
→
Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_0\frac{\sin^{\text{n}}\text{x}}{\sin^\text{n}\text{x}+\cos^\text{n}\text{x}}\text{ dx},\text{ n}\in\text{N}$
→
Find the value of x for which the matrix product
$\begin{bmatrix}2&0&7\\0&1&0\\1&-2&1\end{bmatrix}\begin{bmatrix}-\text{x}&14\text{x}&7\text{x}\\0&1&0\\\text{x}&-4\text{x}&-2\text{x}\end{bmatrix}$ equal an identity matrix.
→
$\text{If y}=\cos^{-1}\bigg(\frac{3\text{x}+4\sqrt{1-\text{x}^2}}{5}\bigg),\ \text{find}\ \frac{\text{dy}}{\text{dx}}\dot{}$
→
If y = $\frac{\sin^{-1}\text{x}}{\sqrt{\text{1 - x}^{2}}}$ show that
$(1-\text{x}^{2})\frac{\text{d}^{2}\text{y}}{\text{dx}}-\text{3x}\frac{\text{dy}}{\text{dx}}-\text{y}=0.$
→
Evaluate the following intregals:
$\int\frac{1}{\text{x}\log\text{x}(2+\log\text{x})}\text{ dx}$
→
Find the distance of the point with position vector $-\hat{\text{i}}-5\hat{\text{j}}-10\hat{\text{k}}$ from the point of intersection of the line $\vec{\text{r}}=(2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}})+\lambda(3\hat{\text{i}}+4\hat{\text{j}}+12\hat{\text{k}})$ with the plane $\vec{\text{r}}.(\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}})=5.$
→