Question

In the given case below find

a) The order of matrix M.

b) The matrix M

`M xx [(1,1),(0, 2)] = [1, 2]`

Answer 1

We know, the product of two matrices is defined only when the number of columns of the first matrix is equal to the number of rows of the second matrix

Let the order of matrix M be a x b.

`M_(a xx b) xx [(1,1),(0, 2)]_(2 xx 2) = [(1, 2)]_(1 xx 2)`

Clearly, the order of matrix M is `1 xx 2`

Let M = [a, b]

`M xx [(1, 1),(0, 2)] = [(1, 2)]`

`[a, b] xx [(1, 1),(0, 2)] = [(1, 2)]`

`[(a + 0, a + 2b )] = [1, 2]`

Comparing the corresponding elements we get

`a = 1 and a + 2b = 2 => 2b = 2 - 1 = 1 => b = 1/2`

`∴ M = [(a, b)] = [(1, 1/2)]`