Multiplication of matrices
Multiplication of matrices
Last updated at March 30, 2023 by Teachoo
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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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)
