Class 12 Maths

# Matrices

## NCERT Solution

### Exercise 1 Part 1

Question 1: In the matrix A = \begin{bmatrix}2 & 5 & 19 & -7\\35 & -2 & 5/2 & 12\\√3 & 1 & -5 & 17\end{bmatrix} write:

(i) The order of the matrix,

(ii) The number of elements,

(iii) Write the elements a13, a21, a33, a24, a23.

Solution:

(i) Since, the given matrix A has three rows and four columns, thus, order of the matrix = 3 x 4

(ii) The given matrix A has 3 x 4 = 12 elements

(iii) a13 = 19, a21 = 35, a33 = –5, a24 = 12, a23 = 5/2.

Question -2 – If a matrix has 24 elements, what are the possible orders it can have? What if it has 13 elements.

Solution: Since, a matrix is of order m x n has mn elements, thus, possible orders of the having 24 elements will be 1 x 24, 2 x 12, 3 x 8, 4 x 6, 6 x 4, 8 x 3, 12 x 2 and 24 x 1.

Matrix having 13 elements has possible orders are 1 x 13 and 13 x 1

Question: 3 – If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

Solution: Possible orders of matrix having 18 elements are 1 x 18, 2 x 9, 3 x 6, 6 x 3, 9 x 2, 18 x 1.

Similarly, possible orders of a matrix having 5 elements are 1 x 5 and 5 x 1

Question 4: Construct a 2xx2 matrix, A=[a_(ij)] whose elements are given by:

1. a_(ij)=((i+j)^2)/2
2. a_(ij)=i/j
3. a_(ij)=((i+2j)^2)/2

Solution: Let A_(2xx2)=\begin{bmatrix}a_(11) & a_(12)\\ a_(21) & a_(22) \end{bmatrix}

(i) a_(ij)=((i+j)^2)/2

So, a_(11)=((1+1)^2)/2=4/2=2
Similarly, a_(12)=((2+1)^2)/2=9/2
a_(21)=((2+1)^2)/2=9/2
a_(22)=((2+2)^2)/2=8

So, the required matrix can be given as follows:
\begin{bmatrix}2 & 9/2\\ 9/2 & 8\end{bmatrix}

(ii) a_(ij)=i/j

Solution: a_(11)=1/1=1

a_(12)=1/2

a_(21)=2/1=2

a_(22)=2/2=1

So, the required matrix can be given as follows:

\begin{bmatrix}1 & ½\\2 & 1\end{bmatrix}

(iii) a_(ij)=((i+2j)^2)/2

Solution: a_(11)=((1+2xx1)^2)/2=((1+2)^2)/2=9/2

a_(12)=((1+2xx2)^2)/2=((1+4)^2)/2=(25)2

a_(21)=((2+2xx1)^2)/2=((2+2)^2)/2=(16)/2=8

a_(22)=((2+2xx2)^2)/2=((2+4)^2)/2=(36)/2=18

So, the required matrix can be given as follows:

\begin{bmatrix}9/2 & 25/2\\8 & 18\end{bmatrix}