If a, b, c are in A.P, find the value of \(\left| \begin{matrix} 2y+4 & \quad 5y+7 & 8y+a \\ 3y+5 & 6y+8 & 9y+b \\ 4y+6 & 7y+9 & 10y+c \end{matrix} \right| \)

Show that the matrix A =\(\left[ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{matrix} \right] \)satisfies the equation A² - 4A - 5I₃ = 0 and hence find A^-1.

Use the product \(\left[ \begin{matrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{matrix} \right] \left[ \begin{matrix} -2 & 0 & 1 \\ 9 & 2 & -3 \\ 6 & 1 & -2 \end{matrix} \right] \)to solve the system of equations x - 2y + 2z = 1, 2y - 3z = 1, 3x - 2y + 4z = 2.

Two types of radio values A, B are available and two types of radios P and Q are assembled in a small factory. The factory uses 2 valves of type A and 3 valves of type B for the type B for the type of radio P, and for the radio Q it uses 3 valves of type A and 4 valves of type B. If the number of valves of type A and B used by the factory are 130 and 180 respectively, find out the number of radios assembled use matrix method.

An amount of Rs. 5000 is put into three investment at the rate of interest of 6%, 7% and 8% per annum respectively. The total annual income is Rs. 358. If the combined income from the first two investment is Rs. 70 more than the income from the third, find the amount of each investment by matrix method.