Download App

MATRICES — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMATRICES2 Marks
Question
Let $\text{A}=\begin{bmatrix}1&2\\-1&3\end{bmatrix},\ \text{B}=\begin{bmatrix}4&0\\1&5\end{bmatrix},$ $\text{C}=\begin{bmatrix}2&0\\1&-2\end{bmatrix},$ a = 4, b = -2, then show that $(\text{bA})^{\text{T}}=\text{bA}^{\text{T}}.$
✓

Answer

We have, $\text{A}=\begin{bmatrix}1&2\\-1&3\end{bmatrix},\ \text{B}=\begin{bmatrix}4&0\\1&5\end{bmatrix},$ $\text{C}=\begin{bmatrix}2&0\\1&-2\end{bmatrix},$ and a = 4, b = -2$(\text{bA})^{\text{T}}=\begin{bmatrix}-2&2\\-4&-6\end{bmatrix}\ [\because\ \text{b}=-2]$
$=\begin{bmatrix}-2&2\\-4&-6\end{bmatrix}$
and $\text{A}^{\text{T}}=\begin{bmatrix}1&-1\\2&3\end{bmatrix}$ $\therefore\ \text{bA}^{\text{T}}=\begin{bmatrix}-2&2\\-4&-6\end{bmatrix}=(\text{bA})^{\text{T}}$ Hence proved.

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 MATRICES→MATRICES — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},\ \vec{\text{b}}=4\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$and $\vec{\text{c}}=\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}$, find a vecctor of magnitude 6 units which is parallel to the vector $2\vec{\text{a}}-\vec{\text{b}}+3\vec{\text{c}}$.
→
Find the adjoint matrix of matrix $\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$.
→
If $\begin{bmatrix}\text{a }-\text{b}&2\text{a}+\text{c}\\2\text{a}-\text{b}&3\text{c}+\text{d} \end{bmatrix}=\begin{bmatrix}-1&5\\0&13 \end{bmatrix},$ fine the value of b.
→
For what value of $\lambda$ are the vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ perpendicular to each other if 
$\vec{\text{a}}=\lambda\hat{\text{i}}+3\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$
→
Integrate the function: $e^{2 x+3}$
→
With the help of integration find the complete area of circle $x^2+y^2=1$.
→
Evaluate the following integrals:
$\int\frac{1}{1+\cos2\text{x}}\text{dx}$
→
If $|A| = 2,$ where $A$ is $2 \times 2$ matrix, find $|$adj $A|.$
→
Integrate the function: $\sqrt{a x+b}$
→
Find the sum of the vectors: $\vec a = \hat i - 2\hat j + \hat k,\vec b = - 2\hat i + 4\hat j + 5\hat k$ and $\vec c = \hat i - 6\hat j - 7\hat k$
→