Download App

Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\text{A}=\begin{bmatrix}9&1\\7&8\end{bmatrix},\text{ B}=\begin{bmatrix}1&5\\7&12\end{bmatrix},$ find matrix C such that 5A + 3B + 2C is a null matrix.
✓

Answer

Given, $5\text{A}+3\text{B}+2\text{C}=\begin{bmatrix}0&0\\0&0\end{bmatrix}$
$\Rightarrow5\begin{bmatrix}9&1\\7&8\end{bmatrix}+3\begin{bmatrix}1&5\\7&12\end{bmatrix}+2\text{C}=\begin{bmatrix}0&0\\0&0\end{bmatrix}$
$\Rightarrow\begin{bmatrix}45&5\\35&40\end{bmatrix}+\begin{bmatrix}3&15\\21&36\end{bmatrix}+2\text{C}\begin{bmatrix}0&0\\0&0\end{bmatrix}$
$\Rightarrow\begin{bmatrix}45+3&5+15\\35+21&40+36\end{bmatrix}+2\text{C}=\begin{bmatrix}0&0\\0&0\end{bmatrix}$
$\Rightarrow\begin{bmatrix}48&20\\56&76\end{bmatrix}+2\text{C}=\begin{bmatrix}0&0\\0&0\end{bmatrix}$
$\Rightarrow2\text{C}=\begin{bmatrix}0&0\\0&0\end{bmatrix}-\begin{bmatrix}48&20\\56&76\end{bmatrix}$
$\Rightarrow\text{C}=\frac{1}{2}\begin{bmatrix}-48&-20\\-56&-76\end{bmatrix}$
$\Rightarrow\text{C}=​​\begin{bmatrix}-24&-10\\-28&-38\end{bmatrix}$

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 Questions" 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

Evaluate the following integrals:
$\int\frac{\sin^3\text{x}-\cos^3\text{x}}{\sin^2\text{x}\cos^2\text{x}}\text{dx}$
→
Find the general solution of the differential equation $\left( {{e^x} + {\text{ }}{e^{ - x}}} \right){\text{ }}dy{\text{ }} - {\text{ }}\left( {{e^x} - {\text{ }}{e^{ - x}}} \right){\text{ }}dx{\text{ }} = {\text{ }}0$
→
Evaluate $\int\frac{1}{\text{x}^2+16}\text{ dx}$
→
Find the manitude of two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ that are of the same magnitude, are inclined at 60° and whose scalar product is $\frac{1}{2}.$
→
Find the value of x, if $\begin{bmatrix}3\text{x+y}&-\text{y}\\2\text{y}-\text{x}&3 \end{bmatrix}=\begin{bmatrix}1&2\\-5&3 \end{bmatrix}$
→
Write the position vector of a point dividing the line segment joining points A and B with position vectors $\vec{\text{a}}\text{ and }\vec{\text{b}}$ externally in the ratio 1 : 4, where $\vec{\text{a}}=2\hat{\text{i}}+3\hat{\text{j}}+4\hat{\text{k}}$ and $\vec{\text{b}}=-\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$.
→
If $A$ has order 3 square matrix and $|A|=9$, then find value of $|2 \operatorname{adj} A |$.
→
Let * be a binary operation on Q - {-1} defined by a * b = a + b + ab for all a, b ∈ Q - {-1}. Then,
Find the identity element in Q − {−1}.
→
If $f : C → C$ is defined by $f(x) = x^2$, write $f^{-1}(-4)$. Here, C denotes the set of all complex numbers.
→
Find AB, if $A=\left[\begin{array}{ll} {6} & {9} \\ {2} & {3} \end{array}\right] \text { and } B=\left[\begin{array}{lll} {2} & {6} & {0} \\ {7} & {9} & {8} \end{array}\right]$
→