Download App

Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices3 Marks
Question
If $\text{A}=\begin{bmatrix}2&3\\5&7\end{bmatrix},\text{ B}=\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix},\text{C}=\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix},$ find

2B + 3A and 3C - 4B.

✓

Answer

$2\text{B}+3\text{A}=2\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix}+3\begin{bmatrix}2&3\\5&7\end{bmatrix}$
It is not possible to add these matrices because the number of elements in B are not equal to the number of elements in A. So, 2B + 3A does not exist.
$\Rightarrow3\text{C}-4\text{B}=3\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix}-4\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}-3&6&9\\6&3&0\end{bmatrix}-\begin{bmatrix}-4&0&8\\12&16&4\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}-3+4&6-0&9-8\\6-12&3-16&0-4\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}1&6&1\\-6&-13&-4\end{bmatrix}$

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" 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

Using vectors show that the points A(-2, 3, 5), B(7, 0, -1), C(-3. -2, -5) and D(3, 4, 7) are such that AB and CD intersect at the point P(1, 2, 3).
→
Find the mean and standard deviation of the following probability distributions:
xi 1 2 3 4
pi 0.4 0.3 0.2 0.1
→
Determine whether the below relation is reflexive, symmetric and transitive: 
Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y) : y is divisible by x}
→
Using vector method prove that in any triangle ABC,
$
\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} .
$
→
Solve:
$\sin\Big(\sin^{-1}\frac{1}{5}+\cos^{-1}\text{x}\Big)=1$
→
Differential equation $\text{x}\frac{\text{dy}}{\text{dx}}=1,\text{y}(1)=0$

Function $\text{y}=\log\text{x}$

→
By Using properties of definite integral, evaluate the following integral in Exercise:
$\int^{\text{a}}_{0}\frac{\sqrt{\text{x}}}{\sqrt{\text{x}+\sqrt{\text{a}-\text{x}}}}\text{dx}$
→
Reduce the equation of the following planes to intercept from and find the intercepts on the coordinate axes:
2x - y + z = 5
→
Write a value of $\int\frac{\sin\text{x}-\cos\text{x}}{\sqrt{1+\sin2\text{x}}}\text{ dx}$
→
Find the area of a triangle whose vertices are $A(1,1,1), B(1,2,3)$ and $C(2,3,3)$.
→