Download App

MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES3 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 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

A vector $\vec{\text{r}}$ is inclined to x-axis at 45º and y-axis at 60º. If $|\vec{\text{r}}|=8$ units, find $\vec{\text{r}}$.
→
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=[\text{x}]\text{ for }-1\leq\text{x}\leq1,$ where [x] denotes the greatest integer not exceeding x.
→
Let S be the set of all rational numbers of the for $\frac{\text{m}}{\text{n}},$ where $\text{m}\in\text{Z}$ and n = 1, 2, 3. Prove that * on sdefined by a * b = ab is not a binary operation.
→
Classify the following functions as injection, surjection or bijection:
$f : N \rightarrow N$ given by $f(x) = x^3$​​​​​​​
→
Find the value of $\int \frac{1}{\sqrt{\sin ^3 x \sin (x+\alpha)}} d x$.
→
Find the value of $\lambda$ so that the following vectors are coplanar:
$\vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}++\hat{\text{k}},\vec{\text{b}}=\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}},\vec{\text{c}}=\lambda\hat{\text{i}}+\lambda\hat{\text{j}}+5\hat{\text{k}}$
→
Prove the following: $\cot^{-1}\Bigg[\frac{\sqrt{\text{1 + sin x}}+\sqrt{\text{1 - sin x}}}{\sqrt{\text{1 + sin x }}-\sqrt{\text{1 - sin x}}}\Bigg]=\frac{\text{x}}{2},\text{x}\in\Bigg(0,\frac{\pi}{4}\Bigg)$.
→
Evaluate the definite integral: $\int_1^2 e^{2 x}\left(\frac{1}{x}-\frac{1}{2 x^2}\right) d x$
→
Show that the line through points $(1, -1, 2)$ and $(3, 4, -2)$ is perpendicular to the line throught the points $(0, 3, 2)$ and $(3, 5, 6).$
→
Write the angle between the lines whose direction ratios are perportional to 1, -2, 1 and 4, 3, 2.
→