Multiplication of matrices

Chapter 3 Class 12 Matrices
Concept wise

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

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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)