Question

Let M$\times \left[\begin{array}{cc}1& 1\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}1& 2\end{array}\right]$, where M is a matrix.

a) State the order of the matrix M.

b) Find the matrix M

Answer 1

For matrix multiplication, the number of columns of the $1^{st}$ matrix should be equal to the number of rows of $2^{nd}$ matrix. So the number of columns of M = 2. Since the product of the matrix is 1 $\times$ 2, so the number of rows of M = 1.

Hence its order = 1 $\times$ 2

$\to$ [a b] $\left[\begin{array}{cc}1& 1\\ 0& 2\end{array}\right]$=(1 2)

[a $\times$ 1 + b $\times$ 0 a $\times$1 + b $\times$ 2] = [1 2]

[a a +2b] = [1 2]

By comparing corresponding elements, we get a= 1 and b =$\frac{1}{2}$

Therefore M = [ 1 $\frac{1}{2}$]