#### Matrices And Determinants Important Questions

11th Standard

Reg.No. :
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Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. The value of x, if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

(a)

0, - 1

(b)

0, 1

(c)

- 1, 1

(d)

- 1, - 1

2. The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

(a)

abc

(b)

0

(c)

a2b2c2

(d)

-abc

3. If A is a square matrix of order 3, then |kA| is

(a)

k|A|

(b)

-k|A|

(c)

k3|A|

(d)

-k3|A|

4. Which of the following matrix has no inverse

(a)

$\begin{pmatrix} -1 & 1 \\ 1 &-4 \end{pmatrix}$

(b)

$\begin{pmatrix} 2 & -1 \\ -4 &2 \end{pmatrix}$

(c)

$\begin{pmatrix} cos\ a & sin\ a \\ -sin\ a & cos\ a \end{pmatrix}$

(d)

$\begin{pmatrix} sin\ a & cos\ a \\ -cos\ a & sin\ a \end{pmatrix}$

5. If A = $\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix}$ then |2A| is equal to

(a)

4 cos 2 $\theta$

(b)

4

(c)

2

(d)

1

6. 5 x 2 = 10
7. The technology matrix of an economic system of two industries is$\begin{bmatrix} 0.50 & 0.30 \\ 0.41 & 0.33 \end{bmatrix}$. Test whether the system is viable as per Hawkins Simon conditions.

8. The technology matrix of an economic system of two industries is$\begin{bmatrix} 0.6 & 0.9 \\ 0.20 & 0.80 \end{bmatrix}$ .Test whether the system is viable as per Hawkins-Simon conditions.

9. Solve:$\begin{vmatrix}7&4&11\\-3&5&x\\-x&3&1 \end{vmatrix}=0$

10. Using the property of determinant, evaluate $\begin{vmatrix} 6 &5 &12 \\ 2 & 4 &4 \\2 & 1 & 4 \end{vmatrix}.$

11. Evaluate:$\left| \begin{matrix} 1 & 2 & 4 \\ -1 & 3 & 0 \\ 4 & 1 & 0 \end{matrix} \right|$

12. 5 x 3 = 15
13. Show that $\begin{vmatrix}0 &ab^2 &ac^2 \\a^2b & 0 & bc^2\\a^2c&b^2c&0\end{vmatrix}=2a^3b^3c^3.$

14. If A $= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}$ show that A2-4A+5I2 = 0 and also find A-1.

15. Using matrix method, solve x+2y+z=7, x+3z = 11 and 2x-3y =1.

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

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

18. 4 x 5 = 20
19. Evaluate:$\begin{vmatrix} 1&a&a^2-bc\\1&b&b^2-ca\\1&c&c^2-ab \end{vmatrix}$

20. Solve by using matrix inversion method: x - y + z = 2; 2x- y = 0 , 2y - z = 1.

21. If $A=\left[ \begin{matrix} 1 & tan\quad x \\ -tan\quad x & \quad \quad \quad 1 \end{matrix} \right]$, then show that ATA-1=$\left[ \begin{matrix} cos\quad 2x & -sin2x \\ sin\quad 2x & cos2x \end{matrix} \right] .$

22. 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.