#### Matrices And Determinants Three Marks

11th Standard

Reg.No. :
•
•
•
•
•
•

Time : 00:45:00 Hrs
Total Marks : 30
10 x 3 = 30
1. Using matrix method, solve x+2y+z=7, x+3z = 11 and 2x-3y =1.

2. if A=$\left[ \begin{matrix} cos\ \alpha & sin\ \alpha \\ -sin\ \alpha & \ cos\ \alpha \ \end{matrix} \right]$ is such that AT = A-1, find $\alpha$

3. Write the minors and co-factors of the elements of $\begin{vmatrix}5 & 3 \\-6 & 2\end{vmatrix}$

4. Verify that A(adj A) = (adj A) A = IAI·I for the matrix A = $\begin{bmatrix}2 & 3 \\-1 & 4\end{bmatrix}$

5. Find the inverse of $\begin{bmatrix}-1 & 5 \\-3 & 2 \end{bmatrix}.$

6. Solve: 2x+ 5y = 1 and 3x + 2y = 7 using matrix method.

7. The data below are about an economy of two industries P and Q. The values are in lakhs of rupees.

Producer User Final Demand Total output
P Q
P 16 12 12 40
Q 12 8 4 24

Find the technology matrix and check whether the system is viable as per Hawkins-Simon conditions.

8. Using co-factors of elements of  second column evaluate $\left| \begin{matrix} 6 & -1 & 5 \\ 3 & 0 & 4 \\ -2 & 7 & -3 \end{matrix} \right|$

9. Find the adjoint of the matrix $\left[ \begin{matrix} 2 & -1 & 3 \\ 0 & 5 & 1 \\ 3 & 6 & 8 \end{matrix} \right]$

10. Find the numbers a and b such that A2+aA+bI=0 for the matrix A=$\begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}$