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To multiply two matrices,

44.jpg

 

We first write their order

Multiplication of Matrix - Part 2

For multiplication

Multiplication of Matrix - Part 3

Since 2 ≠ 3

We cannot multiply them

 

But, if we multiply BA

Multiplication of Matrix - Part 4

Then,

Multiplication of Matrix - Part 5

 

So, order of matrix after multiplication is

Multiplication of Matrix - Part 6

= 3 × 2

Let’s learn how to multiply them

Multiplication of Matrix - Part 7

So,

     AB was not possible, but BA was possible

Thus, AB ≠ BA

 

Let’s do some more examples

Multiplication of Matrix - Part 8

Multiplication of Matrix - Part 9

So, multiplication is not possible

 

Multiplication of Matrix - Part 10

Multiplication of Matrix - Part 11

 

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Transcript

A = [■8(3&[email protected]&4)] & B = [■8(3&[email protected]&[email protected]&3)] A = [■8(3&[email protected]&4)]_(2 × 2) & B = [■8(3&[email protected]&[email protected]&3)]_(3 × 2) For multiplication 2 × 2 3 × 2 i.e B = [■8(3&[email protected]&[email protected]&3)]_(3 × 2) & A = [■8(3&[email protected]&4)]_(2 × 2) 3 × 2 2 × 2 3 × 2 2 × 2 They cancel out BA = [■8(3&[email protected]&[email protected]&3)]_(3 × 2) [■8(3&[email protected]&4)]_(2 × 2) 3 × 3 + 2 × 1 1 × 3 + 4 × 1 = [■8(9+2&[email protected]+4&[email protected]+3&10+12)]_(3 × 2) [■8(11&[email protected]&[email protected]&22)]_(3 × 2) = [■8(42&[email protected]&[email protected]&28)]_(3 × 2) Multiply [■8(3&[email protected]&[email protected]&3)] & [■8(9&5&[email protected]&8&[email protected]&1&6)] Our matrices are [■8(3&[email protected]&[email protected]&3)]_(3 × 2) [■8(9&5&[email protected]&8&[email protected]&1&6)]_(3 × 3) Since, They are not equal Multiply [■8([email protected]@[email protected][email protected][email protected]−4)] & [■8(0&−2&3&−15&6&−1)] [■8([email protected]@[email protected][email protected][email protected]−4)]_(6 × 1) [■8(0&−2&3&−15&6&−1)]_(1 × 6) = [■8(0&−2&3&−15&6&−[email protected]&−4&6&−30&12&−[email protected]&−18&27&−135&54&−[email protected]&16&−24&120&−48&[email protected]&10&−15&75&−30&[email protected]&8&−12&60&−24&4)] Multiply [■8(0&−2&3&−15&6&−1)] & [■8([email protected]@[email protected][email protected][email protected]−4)] [■8(0&−2&3&−15&6&−1)]_(1 × 6) [■8([email protected]@[email protected][email protected][email protected]−4)]_(6 × 1) = [0−4+27+120−30+4]_(1 × 1) =〖 [117]〗_(1 × 1)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.