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ML Aggarwal Solutions for Class 10 Chapter 8 –
Matrices


Exercise 8.1
1. Classify the following matrices:




Solution:
It is square matrix of order 2




Solution:
It is row matrix of order 1 × 3




Solution:
It is column matrix of order 3 × 1




Solution:
It is a matrix of order 3 × 2




Solution:

, ML Aggarwal Solutions for Class 10 Chapter 8 –
Matrices


It is a matrix of order 2 × 3




Solution:
It is zero matrix of order 2 × 3

2. (i) If a matrix has 4 elements, what are the possible order it can have?

Solution:
It can have 1 × 4, 4 × 1 or 2 × 2 order.

(ii) If a matrix has 4 elements, what are the possible orders it can have?

Solution:
It can have 1 × 8, 8 × 1, 2 × 4 or 4 × 2 order.

3. Construct a 2 × 2 matrix whose elements aij are given by
(i) aij = 2i – j
(ii) aij =i.j

Solution:
(i) Given aij = 2i – j
Therefore matrix of order 2 × 2 is




(ii) Given aij =i.j
Therefore matrix of order 2 × 2 is




4. Find the values of x and y if:

, ML Aggarwal Solutions for Class 10 Chapter 8 –
Matrices




Solution:
Given



Now by comparing the corresponding elements,
2x + y = 5 ….. i
3x – 2y = 4 ….ii
Multiply (i) by 2 and (ii) by 1 we get
4x + 2y = 10 and 3x – 2y = 4
By adding we get
7x = 14
x = 14/7
x=2
Substituting the value of x in (i)
4+y=5
y=5–4
y=1
Hence x = 2 and y = 1

5. Find the value of x if




Solution:
Given



Comparing the corresponding terms of given matrix we get
-y = 2
Therefore y = -2
Again we have

, ML Aggarwal Solutions for Class 10 Chapter 8 –
Matrices


3x + y = 1
3x = 1 – y
Substituting the value of y we get
3x = 1 – (-2)
3x = 1 + 2
3x = 3
x = 3/3
x=1
Hence x = 1 and y = -2

6. If



Find the values of x and y.

Solution:
Given



Comparing the corresponding terms, we get
x+3=5
x=5–3
x=2
Again we have
y–4=3
y=3+4
y=7
Hence x = 2 and y = 7

7. Find the values of x, y and z if




Solution: