Matrix arithmetic Problem set A Answers

1. (a) 3 × 2
2. (b) 1 × 4
3. (c) 3 × 3

1. (a) \(\begin{pmatrix}-3 & 6 \\ -5 & 7\end{pmatrix}\)
2. (b) \(\begin{pmatrix}0.5 & -0.5 \\ 3 & 0.5\end{pmatrix}\)

1. (a) \(\begin{pmatrix}1 & -1 \\ 6 & 1\end{pmatrix}\)
2. (b) \(\begin{pmatrix}-3 & 9 \\ 6 & -5\end{pmatrix}\)
3. (c) Cannot be done: the orders are different (2 × 2 and 2 × 3).
4. (d) \(\begin{pmatrix}6 & -15 \\ 0 & 9\end{pmatrix}\)
5. (e) \(\begin{pmatrix}7 & -22 \\ -18 & 12\end{pmatrix}\)
6. (f) \(\begin{pmatrix}-0.5 & 2 \\ 3 & -1\end{pmatrix}\)

1. (a) \(x = 4,\; y = 5\)
2. (b) \(x = 4,\; y = -4\) or \(x = -4,\; y = 4\)

\(S - D + R = \begin{pmatrix}18 & 5 & 21 \\ 10 & 14 & 11\end{pmatrix}\)

\(1.06\begin{pmatrix}850 & 1200 \\ 640 & 990\end{pmatrix} = \begin{pmatrix}901 & 1272 \\ 678.4 & 1049.4\end{pmatrix}\)

\(\begin{pmatrix}9 & 9 & 11 \\ 13 & 8 & 6\end{pmatrix}\). The first club: 29 against 27.

\(p = 3,\; q = 1\)

\(s = \tfrac{1}{2},\; b = -4,\; t = 5,\; a = 4.5\)