S Chand CLASS 10 Chapter 8 MATRICES Exercise 8 A

 Exercise 8 A

Question 1 

Ans: 

(i) The order of matrix is $2 \times 2$ and the number of elements is 4 

(ii) The order of matrix is $1 \times 2$ and the number of elements is 2

(iii) The order of matrix is $1 \times 4$ and the number of elements is 4 .

(iv)The order of matrix is $3 \times 1$ and the number of elements is 3 

(v) The order of matrix is $3 \times 4$ and the number of elements is 12 .

(vi)The order of matrix is $3 \times 5$ and the number of elements

(vii) The order of matrix is $4 \times 2$ and the number of elements is 8 .

Question 2 

Ans: (i) No, these matrices are not equal equal because their corresponding element are not same.(ii) $\left[\begin{array}{cc}4 & 7 \\ 3 & 2\end{array}\right]$ and $\left[\begin{array}{cc}3+1 & -\sqrt{45} \\ 5-2 & \frac{6}{3}\end{array}\right]$

$\left[\begin{array}{ll}4 & 7 \\ 3 & 2\end{array}\right]$ and $\left[\begin{array}{ll}4 & 7 \\ 3 & 2\end{array}\right]$

These matrices are equal because their corresponding elements are same 

Question 3

Ans: Let the matrix $2 \times 2$ be $A\left[\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right]$.

According to the question,

$\begin{aligned} a_{i j} &=(2 i-j)^{2} \\ a_{11} &=(2 \times 1-1)^{2} \\ &=(2-1)^{2} \\ &=(1)^{2} \\ &=1 . \end{aligned}$

$\begin{aligned} a_{12} &=(2 \times 1-2)^{2} \\ &=(2-2)^{2} \\ &=0 \\ a_{21} &=(2 \times 2-1)^{2} . \\ &=(4-1)^{2} \\ &=(3)^{2} \\ &=9 \end{aligned}$

$\begin{aligned}{9}_{22} &=(2 \times 2-2)^{2} \\ &=(4-2)^{2} \\ &=(2)^{2} \\ &=4 . \\ \therefore \text { Matrix } A &=\left[\begin{array}{ll}1 & 0 \\ 9 & 4\end{array}\right] \end{aligned}$

Question 4

Ans: Given,

$\text { Matrix } B=\left[\begin{array}{cc}3 & 11 \\-5 & 6 \\8 & 0\end{array}\right]$

(i) The order of matrix B is $3 \times 2$

(ii) The elements $a_{12}=11, a_{31}=8, a_{22}=6 .$

(iii) False, matrix B is not a square matrix because no of rows ≠ no. of columns 

Question 5

Ans: (a) A matrix which has 6 elements can be of the following possible orders

$6 \times 1,2 \times 3,3 \times 2,1 \times 6$

(b) A matrix which has 3 rows and 4 columns will have $3 \times 4=12$ elchemts.

Question 6

Ans:

$(i)\left[\begin{array}{cc}x & y \\ -1 & 5\end{array}\right]=\left[\begin{array}{cc}-2 & 0 \\ -1 & 5\end{array}\right]$

On comparing their corresponding elements 

x=-2 and y =0 

(ii) $\left[\begin{array}{ll}x & y\end{array}\right]=\left[\begin{array}{ll}-2 & y\end{array}\right]$

On comparing their corresponding elements 

x=-2 and 

y=4

(iii)

$\left[\begin{array}{cc}2 x & 3 \\0 & y-1\end{array}\right]=\left[\begin{array}{cc}x-4 & 3 \\0 & 5\end{array}\right]$On comparing their corresponding elements,

$\begin{array}{cl}2 x=x-4 & \text { and } y-1=5 \\2 x-x=-4 & \text { and } y=5+1 . \\x=-4 & \text { and } y=6\end{array}$

Question 7

Ans:

 $\left[\begin{array}{ll}p+4 & 2 q-7 \\ s-3 & r+2 s\end{array}\right]=\left[\begin{array}{cc}6 & -3 \\ 2 & 14\end{array}\right]$

On comparing their corresponding elements,

$\begin{array}{ll}P+4=6, & 2 q-7=-3, \quad 5-3=2 \text { and } 8+2 \rho=14 \\p=6-4, & 2 q=-3+2, \quad 5=2+3 \text { and } 8+2 \times 5=14 \\p=2 ., & q=\frac{4}{2}=2 ., 5=5 \text { and } r=14-10=4 \text {. }\end{array}$

Hence p, q , r and s are 2, 2, 4 and 5 respectively

Question 8

Ans: (i) False, because It is Lot compulsary.

(ii) True

(iii) False.

(iv) False.

(v) False.

(vi) False

(ví) True.

Question 9

Ans: Given 

The length width and height of one box are 6,5,10

And that of second box are 5, 2, 8 

and of third box are 7, 3, 3

$\therefore\left[\begin{array}{ccc}6 & 5 & 10 \\ 5 & 2 & 8 \\ 7 & 3 & 3\end{array}\right]$

Question 10

Ans: (i) Given 

Three pupils Akhil, Rajnish and Sudha got marks in three test algebra. Their scores are 

Akhil= 79, 87 ,92 ; Rajnish = 95, 98, 91 and 

Sudha = 76, 88, 77

$\therefore\left[\begin{array}{ccc}79 & 87 & 92 \\ 95 & 98 & 91 \\ 76 & 88 & 77\end{array}\right]$

(ii) The price of a record is $R_{9} .30$, of a blade packet if Rs. $1.50$ and a soap cake is RS. $1.70$.

$\therefore\left[\begin{array}{c}30 \\1.50 \\1.70\end{array}\right]$