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12th Standard EM

Reg.No. :
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Maths

Do not use black pen
Time : 00:20:00 Hrs
Total Marks : 20

Part - A

10 x 2 = 20
1. For any 2 x 2 matrix, if A (adj A) =$\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \end{matrix} \right]$ then find |A|.

2. For the matrix A, if A3 = I, then find A-1.

3. If A is a square matrix such that A3 = I, then prove that A is non-singular.

4. Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

5. Flod the rank of the matrix $\left[ \begin{matrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{matrix} \right]$.

6. Find the rank of the matrix A =$\left[ \begin{matrix} 4 \\ 7 \end{matrix}\begin{matrix} 5 \\ -3 \end{matrix}\begin{matrix} -6 \\ 0 \end{matrix}\begin{matrix} 1 \\ 8 \end{matrix} \right]$.

7. Show that the equations 3x + y + 9z = 0, 3x + 2y + 12z = 0 and 2x + y + 7z = 0 have nontrivial solutions also.

8. Find k if the equations x + 2y + 2z = 0, x - 3y - 3z = 0, 2x + y + kz = 0 have only the trivial solution.

9. Solve : 2x - y = 3, 5x + y = 4 using matrices.

10. Solve 6x - 7y = 16, 9x - 5y = 35 using (Cramer's rule).