Hello! We hope that the questions explained by Teachoo are helping you for your Board exams. If Teachoo has been of any help to you, would you consider making a donation to support us? Please click on this link to support us.
To multiply two matrices,
We first write their order
For multiplication
Since 2 ≠ 3
We cannot multiply them
But, if we multiply BA
Then,
So, order of matrix after multiplication is
=
3 × 2
Let’s learn how to multiply them
So,
AB was not possible, but BA was possible
Thus, AB ≠ BA
Let’s do some more examples
So, multiplication is not possible
Hello! We hope that the questions explained by Teachoo are helping you for your Board exams. If Teachoo has been of any help to you, would you consider making a donation to support us? Please click on this link to support us.
A = [■8(3&2@1&4)] & B = [■8(3&2@1&4@5&3)]
A = [■8(3&2@1&4)]_(2 × 2) & B = [■8(3&2@1&4@5&3)]_(3 × 2)
For multiplication
2 × 2
3 × 2
i.e
B = [■8(3&2@1&4@5&3)]_(3 × 2) & A = [■8(3&2@1&4)]_(2 × 2)
3 × 2
2 × 2
3 × 2
2 × 2
They cancel out
BA = [■8(3&2@1&4@5&3)]_(3 × 2) [■8(3&2@1&4)]_(2 × 2)
3 × 3
+ 2 × 1
1 × 3 + 4 × 1
= [■8(9+2&6+8@3+4&2+16@15+3&10+12)]_(3 × 2)
[■8(11&14@7&18@18&22)]_(3 × 2)
= [■8(42&44@36&49@40&28)]_(3 × 2)
Multiply
[■8(3&2@1&4@5&3)] & [■8(9&5&2@1&8&5@3&1&6)]
Our matrices are
[■8(3&2@1&4@5&3)]_(3 × 2) [■8(9&5&2@1&8&5@3&1&6)]_(3 × 3)
Since,
They are not equal
Multiply
[■8(1@2@9@−8@−5@−4)] & [■8(0&−2&3&−15&6&−1)]
[■8(1@2@9@−8@−5@−4)]_(6 × 1) [■8(0&−2&3&−15&6&−1)]_(1 × 6)
= [■8(0&−2&3&−15&6&−1@0&−4&6&−30&12&−2@0&−18&27&−135&54&−9@0&16&−24&120&−48&8@0&10&−15&75&−30&5@0&8&−12&60&−24&4)]
Multiply
[■8(0&−2&3&−15&6&−1)] & [■8(1@2@9@−8@−5@−4)]
[■8(0&−2&3&−15&6&−1)]_(1 × 6) [■8(1@2@9@−8@−5@−4)]_(6 × 1)
= [0−4+27+120−30+4]_(1 × 1)
=〖 [117]〗_(1 × 1)
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.