Mathematics

Problem

Let

A,B,C

and

D

be matrices of the same order. a. Expand the expression

A(B+C)+A(D-C)

and collect like terms. b. Factorise the result obtained in part (i) to write it in its simplest product form. c. If

A=\begin{pmatrix}1&-1\\2&0\end{pmatrix},\;B=\begin{pmatrix}3&2\\-1&4\end{pmatrix},\;C=\begin{pmatrix}0&5\\2&-3\end{pmatrix},\;D=\begin{pmatrix}-2&1\\3&0\end{pmatrix},

evaluate the matrix found in part (ii).