Exercise 1.1

Let $B$ be a $4\times 4$ matrix to which we apply the following operations:

1.

double column 1,

2.

halve row 3,

3.

add row 3 to row 1,

4.

interchange columns 1 and 4,

5.

subtract row 2 from each of the other rows,

6.

replace column 4 by column 3,

7.

delete column 1 (so that the column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.
(b) Write it again as a product $\mathit{ABC}$ (same $B$) of three matrices.