Download App

Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
Let $\text{A}=\begin{bmatrix}2&4\\3&2\end{bmatrix},\text{B}=\begin{bmatrix}1&3\\-2&5\end{bmatrix}$ and $\text{C}=\begin{bmatrix}-2&5\\3&4\end{bmatrix}.$ Find each of the following:
$3\text{A}-\text{C}$
✓

Answer

Given, $\text{A}=\begin{bmatrix}2&4\\3&2\end{bmatrix},\text{ B}=\begin{bmatrix}1&3\\-2&5\end{bmatrix},\text{ C}=\begin{bmatrix}-2&5\\3&4\end{bmatrix}$
$3\text{A}-\text{C}$
$\Rightarrow3\text{A}-\text{C}=3\begin{bmatrix}2&4\\3&2\end{bmatrix}-\begin{bmatrix}-2&5\\3&4 \end{bmatrix}$
$\Rightarrow3\text{A}-\text{C}=\begin{bmatrix}6&12\\9&6\end{bmatrix}-\begin{bmatrix}-2&5\\3&4 \end{bmatrix}$
$\Rightarrow3\text{A}-\text{C}=\begin{bmatrix}6+2&12-5\\9-3&6-4\end{bmatrix}$
$\Rightarrow3\text{A}-\text{C}=\begin{bmatrix}8&7\\6&2\end{bmatrix}$

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 "2 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

If $\text{f(x)}=\log_\text{e}(\log_\text{e}\text{x}),$ then write the value of f'(e).
→
If $\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k}$ and $\vec{b}=\hat{i}+3 \hat{j}-5 \hat{k}$, then show that the vectors $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$ are perpendicular.
→
If A and B are square matrices of the same order, explain, why in general:
(A + B)(A - B) ≠ A2 - B2.
→
A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ₹ 100 and that on a bracelet is ₹ 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.
→
If $\text{A}=\begin{bmatrix}-1&0&0\\0&-1&0\\0&0&-1\end{bmatrix},$ find A3.
→
Evaluate the following integrals:
$\int\limits^1_0\frac{1}{1+\text{x}^2}\text{ dx}$
→
Write the cartesian and vector equations of y-axis.
→
Write a 2×2 matrix which is both symmetric and skew-symmetric.
→
Give an example of a relation which is transitive but neither reflexive nor symmetric.
→
Differentiate w.r.t. x the function in Exercise:
$\sin^{-1}(\text{x}\sqrt{\text{x)}},\ 0\leq\text{x}\leq1$
→