Download App

Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices2 Marks
Question
If A = $\left[\begin{array}{ccc} {-1} & {2} & {3} \\ {5} & {7} & {9} \\ {-2} & {1} & {1} \end{array}\right]$ and B = $\left[\begin{array}{rrr} {-4} & {1} & {-5} \\ {1} & {2} & {0} \\ {1} & {3} & {1} \end{array}\right]$, then verify (A + B)′ = A′ + B′,
✓

Answer

A = $\left[\begin{array}{ccc} {-1} & {2} & {3} \\ {5} & {7} & {9} \\ {-2} & {1} & {1} \end{array}\right] \text { and } B=\left[\begin{array}{ccc} {-4} & {1} & {-5} \\ {1} & {2} & {0} \\ {1} & {3} & {1} \end{array}\right]$
(A+B)’ = A’+B’
Explanation: We will first calculate L.H.S i.e. (A+B)’ and then consecutively we will calculate R.H.S and verify that both are equal.
So, A + B = $\left[\begin{array}{ccc} {-1} & {2} & {3} \\ {5} & {7} & {9} \\ {-2} & {1} & {1} \end{array}\right]+\left[\begin{array}{ccc} {-4} & {1} & {-5} \\ {1} & {2} & {0} \\ {1} & {3} & {1} \end{array}\right]$
$\Rightarrow A+B=\left[\begin{array}{ccc} {-1+(-4)} & {2+1} & {3+(-5)} \\ {5+1} & {7+2} & {9+0} \\ {-2+1} & {1+3} & {1+1} \end{array}\right]$
$\Rightarrow A+B=\left[\begin{array}{ccc} {-5} & {3} & {-2} \\ {6} & {9} & {9} \\ {-1} & {4} & {2} \end{array}\right]$
Therefore, $(A+B)^\prime=\left[\begin{array}{ccc} {-5} & {6} & {-1} \\ {3} & {9} & {4} \\ {-2} & {9} & {2} \end{array}\right] $ ...(1)
Noe, $A^{\prime}=\left[\begin{array}{ccc} {-1} & {5} & {-2} \\ {2} & {7} & {1} \\ {3} & {9} & {1} \end{array}\right] \text { and } B^{\prime}=\left[\begin{array}{ccc} {-4} & {1} & {1} \\ {1} & {2} & {3} \\ {-5} & {0} & {1} \end{array}\right]$
So, A' + B' = $\left[\begin{array}{ccc} {-1} & {5} & {-2} \\ {2} & {7} & {1} \\ {3} & {9} & {1} \end{array}\right]+\left[\begin{array}{ccc} {-4} & {1} & {1} \\ {1} & {2} & {3} \\ {-5} & {0} & {1} \end{array}\right]$
$\Rightarrow \mathrm{A}^{\prime}+\mathrm{B}^{\prime}=\left[\begin{array}{ccc} {-1+(-4)} & {5+1} & {-2+1} \\ {2+1} & {7+2} & {1+3} \\ {3+(-5)} & {9+0} & {1+1} \end{array}\right]$
$\Rightarrow A^{\prime}+B^{\prime}=\left[\begin{array}{ccc} {-5} & {6} & {-1} \\ {3} & {9} & {4} \\ {-2} & {9} & {2} \end{array}\right] $  ...(2)
From equation (1) &( 2), we see that
(A+B)’ = A’+B’. Hence verified.

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 Matrices→Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find:
$\int\frac{\text{dx}}{5 - \text{8x - x}^{2}}$
→
Write the position vector of a point dividing the line segment joining points having position vectors $\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$ externally in the ratio 2 : 3.
→
Evaluate the following integrals:
$\int\limits^2_02\text{x}\big[\text{x}\big]\text{dx}$
→
Let $\text{f(x)=}\begin{cases}1+\text{x,}&0\leq\text{x}\leq2\\3-\text{x,}&2<\text{x}\leq3\end{cases}.$ Find fof.
→
Find the volume of the parallelopiped with its edges represented by the vectors
$\hat{\text{i}}+\hat{\text{j}},\hat{\text{i}}+2\hat{\text{j}}$ and $\hat{\text{i}}+\hat{\text{j}}+\pi{\text{k}}.$
→
Find the value of $\int \frac{1}{x-\sqrt{x}} d x$.
→
Evaluate the following:
$\cos^{-1}\Big\{\cos\frac{5\pi}{4}\Big\}$
→
Let A = [aij] be a square matrix of order 3 × 3 and Cij denote cofactor of aij in A. if |A| = 5, write the value of a13C13 + a23C23 + a33C33.
→
Evaluate the definite integral $\int_{0}^{1} \frac{2 x+3}{5 x^{2}+1} d x$
→
Write a value of $\int\text{a}^{\text{x}}\text{e}^{\text{x}}\text{ dx}$
→