# Important Questions for Class 12 Chapter 3 - Matrices

To understand a topic clearly, students need to practice related exercises too. Understanding this need, our expert academicians have come up with the Important questions for class 12th students. Download the free CBSE important questions for class 12th and start practicing.

Important questions based on NCERT syllabus for Class 12 Chapter 3 - Matrices:

Question 1: Construct a 3 × 2 matrix whose elements are given by a_{ij} = 1/2 |2i - j|

Solution: In general a 3 × 2 matrix is given by A = a_{11} a_{12}
a_{21} a_{22}
a_{31} a_{32}

Now, a_{ij} = 1/2 |2i - j|, i = 1,2,3 and j = 1, 2

Therefore, a_{11} = 1/2 |2(1) - 1| = 1/2|1| = 1/2
a_{12} = 1/2 |2(1) - 2| = 1/2|0| = 0
a_{21} = 1/2 |2(2) - 1| = 1/2|3| = 3/2
a_{22} = 1/2 |2(2) - 2| = 1/2|2| = 1
a_{31} = 1/2 |2(3) - 1| = 1/2|5| = 5/2
a_{32} = 1/2 |2(3) - 2| = 1/2 | 6 - 2| = 1/2|4| = 1/2

Hence the required matrix is given by
A = 1/2 0
3/2 1
5/2 1/2

Question 2: Write the value of x + 2y - z from the following equation

x + y - z 7
x - z 8
y + z 10

Solution: By definition of equality of matrices i.e., if two matrices are equal then their corresponding elements are equal.

Given
x + y - z 7
x - z 8
y - z 10

on equating the corresponding elements we get,

x + y - z = 7 ..........(1)
x - z = 8........(2)
y - z = 10 ......(3)

Consider equation 1 we get

x + y- z = 7
we can group it as x + (y - z) = 7.....(4)

we know that y - z = 10

Substitute the equation 3 in equation 4 we get

x + (10) = 7 => x = -3

Substitute x value in equation 2 to get value of z

x - z = 8 => -3 - z = 8 => z = -11

Substitute z value in equation 3 to get y value

y - z = 10 => y -(-11) = 10 => y = 10 - 11=> y = -1

Now we have to find the value of x + 2y - z
we know x = -3, y = -1 and z = -11

x + 2y - z = -3 + 2(-1) - 11 = -3 - 2 - 11 = -16

Question 3: If A = -2 4 8 B = 5 6
6 1 0 8 0
1 3
Find AB and BA And prove that \$AB \neq BA\$

Solution: A = -2 4 8 B = 5 6
6 1 0 8 0
1 3
AB = -10+32+8 -12+0+24
30+8+0 36+0+0

AB = 30 12
38 36

BA = 5 6 -2 4 8
8 0 6 1 0
1 3

= -10+36 20+6 40+0
-16+0 32+0 64+0
-2+18 4+3 8+0

= 26 26 40
-16 32 64
16 7 8

Hence \$AB \neq BA\$ = 30 12 \neq 26 26 40
38 36 -16 32 64
16 7 8