Solve: 2x - 3y - 1 = 0, 5x + 2y - 12 = 0 by Cramer's rule.

If \(\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 2 \\ -1 \\ 3 \end{matrix} \right] \) find x,y and z

If \(A=\left( \begin{matrix} 2 & 4 \\ 4 & 3 \end{matrix} \right) ,X=\left( \begin{matrix} n \\ 1 \end{matrix} \right) B=\left( \begin{matrix} 8 \\ 11 \end{matrix} \right) \) and AX = B then find n.

Solve: 2x + 3y = 5, 6x + 5y = 11

Two products A and B currently share the market with shares 60% and 40% each respectively. Each week some brand switching latees place. Of those who bought A the previous week 70% buy it again whereas 30% switch over to B. Of those who bought B the previous week, 80% buy it again whereas 20% switch over to A. Find their shares after one week and after two weeks.