Systems of equations with the inverse matrix Problem set B Answers

1. (a) \(x = 2,\; y = 3\)
2. (b) \(x = 3.5,\; y = -1\)
3. (c) \(x = -1,\; y = -2\)

1. (a) \(x = 2,\; y = 1,\; z = 3\)
2. (b) \(x = 3,\; y = 1,\; z = 2\)

1. (a) \(k = \pm 4\)
2. (b) \(k = \pm 5\)

1. (a) 0
2. (b) k = 6
3. (c) No solutions: the lines are parallel and different.

\(\begin{pmatrix}3 & 2 \\ 5 & 4\end{pmatrix}\begin{pmatrix}s \\ j\end{pmatrix} = \begin{pmatrix}11.1 \\ 19.3\end{pmatrix}\). Sandwich £2.90, juice £1.20.

\(\begin{pmatrix}1 & 1 & 1 \\ -1 & 0 & 1 \\ 0.03 & 0.05 & 0.02\end{pmatrix}\begin{pmatrix}x \\ y \\ z\end{pmatrix} = \begin{pmatrix}60000 \\ 8000 \\ 2010\end{pmatrix}\). X €15 000, Y €22 000, Z €23 000.

\(x = \dfrac{3k - 2}{k^2 - 1},\quad y = \dfrac{2k - 3}{k^2 - 1}\)