Question

Compute the product AB by the definition of the product of​matrices, where Ab1 and Ab2 are computed​ separately, and by the​row-column rule for computing AB.

Matrix A= [2 -2]
[3 4]
[4 -3]

Matrix B =
[4 -1]
[-1 2]

Answer 1

`A * B = \left[\begin{array}{ccc}10&-6\\8&5\\19&-10\end{array}\right]`

Explanation:

Given

`A =\left[\begin{array}{cc}2&-2\\3&4\\4&-3\end{array}\right]`

`B = \left[\begin{array}{cc}4&-1\\-1&2\end{array}\right]`

Required

`AB`

To do this, we simply multiply the rows of A by the column of B;

So, we have:

`A * B = \left[\begin{array}{ccc}2*4 + -2*-1&2*-1+-2*2\\3*4+4*-1&3*-1+4*2\\4*4-3*-1&4*-1-3*2\end{array}\right]`

`A * B = \left[\begin{array}{ccc}10&-6\\8&5\\19&-10\end{array}\right]`