Download App

Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices4 Marks
Question
Solve the matrix equations:
$\begin{bmatrix}\text{x}&1\end{bmatrix}\begin{bmatrix}1&0\\-2&-3\end{bmatrix}\begin{bmatrix}\text{x}\\5\end{bmatrix}=0$
✓

Answer

Here,
$\begin{bmatrix}\text{x}&1\end{bmatrix}\begin{bmatrix}1&0\\-2&-3\end{bmatrix}\begin{bmatrix}\text{x}\\5\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}\text{x}-2&0-3\end{bmatrix}\begin{bmatrix}\text{x}\\5\end{bmatrix}=0$
$ \Rightarrow\begin{bmatrix}(\text{x}-2)\text{x}-15\end{bmatrix} =0$
$\Rightarrow\text{x}^2-2\text{x}-15=0$
$ \Rightarrow\text{x}^2-5\text{x}+3\text{x}-15=0$
$ \Rightarrow\text{x}(\text{x}-5)+3(\text{x}-5)=0$
$\Rightarrow(\text{x}-5)(\text{x}+3)=0$
$ \Rightarrow\text{x}-5=0\ \text{or}\ \text{x}+3=0$
$ \Rightarrow\text{x}=5\ \text{or}\ \text{x}=-3$
So,
$\text{x}=5\text{ or }-3$

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 "4 Marks" 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

$\text{If } x^{\text{m }} \text{y}^{\text{n}} = ({x + \text{y)}^{\text{m + n}}}, \text{prove that} \frac{\text{d}^{2}\text{y}}{\text{d}x^{2}} = 0.$
→
In a hospital, there are 20 kidney dialysis machines and that the chance of any one of them to be out of service during a day is 0.02. Determine the probability that exactly 3 machines will be out of service on the same day.
→
If $ \vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}-2\hat{\text{k}}\ \text{and}\ \vec{\text{b}}=7\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}}, $ then express $ \overrightarrow{\text{b}}$ in the form of $\overrightarrow{\text{b}}=\ \overrightarrow{\text{b}}_1+\overrightarrow{\text{b}}_2,$ where $ \overrightarrow{\text{b}}_1$ is parallel to $\overrightarrow{\text{a}}$ and $ \overrightarrow{\text{b}}_2$ is perpendicular to$\overrightarrow{\text{a}}$.
→
An insurance company insured 2000 scooters and 3000 motorcycles. The probability of an accident involving a scooter is 0.01 and that of a motorcy is 0.02. An insured vehicle met with an accident. Find the probability that the accidented vehicle was a motorcycle.
→
$\int\sin^{-1}\sqrt{\frac{\text{x}}{\text{a}+\text{x}}}\text{dx}$
Hint: Put $\text{x} = \text{a}\tan^2θ$
→
 Prove that the area common to tha two parabola y = 2x2 and y = x2 + 4 is 323 sq. units.
→
Show that the lines $\vec{\text{r}}=(\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}})+\lambda(3\hat{\text{i}}-\hat{\text{j}})\ \text{and}\ \vec{\text{r}}=({4\hat{\text{i}}-\hat{\text{k}})+\mu(2\hat{\text{i}}+3\hat{\text{k}}})$intersect. Also find their point of intersection.
→
Compute the adjoint of the following matrices:

$\begin{bmatrix}2 & -1 & 3 \\4 & 2 & 5 \\ 0 & 4 & -1 \end{bmatrix}$

Verify that (adj A)A = |A|I = A (adj A) for the above matrices.

→
Solve the differential equation: $(\text{x}+1)\frac{\text{dy}}{\text{dx}}=2\text{e}^{-\text{y}}-1;\ \text{y(0)}=0.$
→
A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one bybone without replacement. What is the probability that at least one of the three marbles drawn be black, if the first marble is red?
→