Download App

MATRICES — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMATRICES5 Marks
Question
Evaluate the following:
$\begin{bmatrix}1&-1\\0&2\\2&3\end{bmatrix}\begin{pmatrix}\begin{bmatrix}1&0&2\\2&0&1\end{bmatrix}-\begin{bmatrix}0&1&2\\1&0&2 \end{bmatrix}\end{pmatrix}$
✓

Answer

$\begin{bmatrix}1&-1\\0&2\\2&3\end{bmatrix}\begin{pmatrix}\begin{bmatrix}1&0&2\\2&0&1\end{bmatrix}-\begin{bmatrix}0&1&2\\1&0&2 \end{bmatrix}\end{pmatrix}$
$=\begin{bmatrix}1&-1\\0&2\\2&3\end{bmatrix}\begin{pmatrix}\begin{bmatrix}1-0&0-1&2-2\\2-1&0-0&1-2 \end{bmatrix}\end{pmatrix}$
$=\begin{bmatrix}1&-1\\0&2\\2&3\end{bmatrix}\begin{bmatrix}1&-1&0\\1&0&1\end{bmatrix}$
$=\begin{bmatrix}1-1&-1+0&0+1\\0+2&0+0&0-2\\2+3&-2+0&0-3\end{bmatrix}$
$=\begin{bmatrix}0&-1&1\\2&0&-2\\5&-2&-3\end{bmatrix}$
Hence,
$\begin{bmatrix}1&-1\\0&2\\2&3\end{bmatrix}\begin{pmatrix}\begin{bmatrix}1&0&2\\2&0&1\end{bmatrix}-\begin{bmatrix} 0&1&2\\1&0&2\end{bmatrix} \end{pmatrix}\begin{bmatrix}0&-1&1\\2&0&-2\\5&-2&-3\end{bmatrix}$

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 "5 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

Evaluate the following integrals as limit of sum:
$\int\limits^2_{1}\text{x}^2\text{ dx}$
→
Find the area of the smaller region bounded by the ellipse $\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1$ and the line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1.$
→
Differentiate the following functions with respect to x:
$(\text{x}\cos\text{x})^\text{x}+(\text{x}\sin\text{x})^\frac{1}{\text{x}}$
→
Maximize Z = 4x + 3y
Subject to
$3\text{x}+4\text{y}\leq24$
$8\text{x}+6\text{y}\leq48$
$\text{x}\leq5$
$\text{y}\leq5$
$\text{x},\text{y}\geq0$
→
A manufacturer can produce two products, A and B, during a given time period. Each of these products requires four different manufacturing operations: grinding, turning, assembling and testing. The manufacturing requirements in hours per unit of products A and B are given below.
 
A
B
Grinding
1
2
Turning
3
1
Assembling
6
3
Testing
5
4
The available capacities of these operations in hours for the given time period are: grinding 30; turning 60, assembling 200; testing 200. The contribution to profit is Rs 20 for each unit of A and Rs 30 for each unit of B. The firm can sell all that it produces at the prevailing market price. Determine the optimum amount of A and B to produce during the given time period. Formulate this as a LPP.
→
Find the inverse of each of the matrix:
$\begin{bmatrix}1&-1&2\\0&2&-3\\3&-2&4\end{bmatrix}$
→
A fruit grower can use two types of fertilizer in his garden, brand $P$ and $Q.$ The amounts $($in $\ kg)$ of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least $240\ kg$ of phosphoric acid, at least $270\ kg$ of potash and at most $310\ kg$ of chlorine.
Kg per bag
 
Brand $P$
Brand $P$
Nitrogen
 $32$ $3.5$
Phosphoric
 $1$ $2$
Potash
 $3$ $1.5$
Chlorine
 $1.5$ $2$
If the grower wants to minimize the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden?
→
Find values of $k,$ if area of triangle is $4$ square units whose vertices are:
$(-2, 0), (0, 4), (0, k)$
→
Let $R$ be relation defined on the set of natural number $N$ as follows: $R=\{(x, y): x \in N, y \in N, 2 x+y=41\}$ Find the domain and range of the relation $R$. Also verify whether $R$ is reflexive, symmetric and transitive.
→
Find the area of the region in the first quadrant enclosed by the $x-$axis, the line $y = x$ and the circle $x^2+ y^2 = 32.$
→