Download App

Algebra of Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAlgebra of Matrices5 Marks
Question
Solve the matrix equations:
$\begin{bmatrix}2\text{x}&3\end{bmatrix}\begin{bmatrix}1&2\\-3&0\end{bmatrix}\begin{bmatrix}\text{x}\\8\end{bmatrix}=0$
✓

Answer

$\begin{bmatrix}2\text{x}&3\end{bmatrix}\begin{bmatrix}1&2\\-3&0\end{bmatrix}\begin{bmatrix}\text{x}\\8\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}2\text{x}-9&4\text{x}\end{bmatrix}\begin{bmatrix}\text{x}\\8\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}\text{x}(2\text{x}-9)+32\text{x}\end{bmatrix}=0$
$ \Rightarrow\begin{bmatrix}2\text{x}^2-9\text{x}+32\text{x}\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}2\text{x}^2+23\text{x}\end{bmatrix}=0$
$\Rightarrow2\text{x}^2+23\text{x}=0$
$\Rightarrow\text{x}(2\text{x}+23)=0$
$\Rightarrow\text{x}=0\ \text{or }\text{x}=-\frac{23}{2}$
$\therefore\ \text{x}=0\ \text{or }\text{x}=-\frac{23}{2}$

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 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

Evaluate the following integrals:
$\int\frac{\text{e}^{\text{m}\sin^{-1}\text{x}}}{\sqrt{1-\text{x}^2}}\text{ dx}$
→
Find the points of discontinuity, if any of the following function:
$\text{f(x)}=​​\begin{cases}\sin\text{x}-\cos\text{x},&\text{if }\text{ x}\neq0\\-1,&\text{if }\text{ x}=0\end{cases}$
→
Evaluate the following integrals:
$\int\frac{\text{x}^2}{1-\text{x}^4}\ \text{dx}$
→
Using integration, find the area of the region enclosed by the parabola $y = 3x^2$ and the line $3x - y + 6 = 0.$
→
$\text{If A} = \begin{bmatrix} 0 & 6 & 7 \\ -6 & 0 & 8 \\ 7 & -8 & 0 \end{bmatrix}, \text{B} = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 2 \\ 1 & 2 & 0 \end{bmatrix}, \text{C} = \begin{bmatrix} 2 \\ -2 \\ 3 \end{bmatrix},$ then calculate AC, BC and (A + B) C. Also verify that (A + B) C = AC + BC.
→
If $\vec{\text{a}},\vec{\text{ b}}$ and $\vec{\text{c}}$ determine the vertices of a triangle, show that $\frac{1}{2}[\vec{\text{b}}\times\vec{\text{c}}+\vec{\text{c}}\times\vec{\text{a}}+\vec{\text{a}}\times\vec{\text{b}}]$ gives the vector area of the triangle. Hence, deduce the condition that the three points $\vec{\text{a}},\vec{\text{ b}}$ and $\vec{\text{c}}$ are collinear. Also, find the unit vector normal to the plane of the triangle.
→
Prove that: $\begin{vmatrix}\text{a}^2+1&\text{ab}&\text{ac}\\\text{ab}&\text{b}^2+1&\text{bc}\\\text{ca}&\text{cb}&\text{c}^2+1 \end{vmatrix}=1+\text{a}^2+\text{b}^2+\text{c}^2$
→
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.
$\text{f}(\text{x})=\tan^{-1}\text{x}\text{ on }[0,1]$
→
Two tailors, $A$ and $B$ earn $Rs. 15$ and $Rs. 20$ per day respectively. $A$ can stitch $6$ shirts and $4$ pants while $B$ can stitch $10$ shirts and $4$ pants per day. How many days shall each work if it is desired to produce $($at least$) 60$ shirts and $32$ pants at a minimum labour cost?
→
Solve the following differential equation:
$(\text{x}+2\text{y})\text{dx}-(2\text{x}-\text{y})\text{dy}=0$
→