Question
If $\text{A}=\begin{bmatrix}2&3\\5&7\end{bmatrix},\text{ B}=\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix},\text{C}=\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix},$ find2B + 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.
$\Rightarrow3\text{C}-4\text{B}=3\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix}-4\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}-3&6&9\\6&3&0\end{bmatrix}-\begin{bmatrix}-4&0&8\\12&16&4\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}-3+4&6-0&9-8\\6-12&3-16&0-4\end{bmatrix}$
$\Rightarrow3\text{C}-4\text{B}=\begin{bmatrix}1&6&1\\-6&-13&-4\end{bmatrix}$
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.
Explore more
Similar questions
Find the co-ordinates of the points of intersection of the lines represented by $x^2-y^2-2 x+1$ = 0.
→Find k ifThe slope of one of the lines given by $3 x^2-4 x y+k y^2=0$ is 1 .
→Evaluate the following:
→$\int_0^1 \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x$
Differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{y}=0,\text{y}(0)=0,\text{y}'(0)=1$Function $\text{y}=\sin\text{x}$
→A circular disc of radius 3cm is being heated. Due to expansion, its radius increases at the rate of 0.05cm/ sec. Find the rate at which its area is increasing when radius is 3.2cm.
Find the value of $\cos ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{4}{5}\right)$
→Find the equation of rthe planes parallel to the plane x + 2y - 2z + 8 = 0 that are at a distance of 2 units from the point (2, 1, 1).
Diffrentiate the following w. r. t. x.$\sin ^{-1}\left(\frac{\cos \sqrt{x}+\sin \sqrt{x}}{\sqrt{2}}\right)$
→Express the following switching circuit in the symnolic from of logic,. Construct the switching table :
If $\text{A}=\begin{bmatrix}\cos\alpha&\sin\alpha\\-\sin\alpha&\cos\alpha\end{bmatrix},$ then verify that $A^TA = I_2$.
→