#### Matrices And Determinants Book Back Questions

11th Standard

Reg.No. :
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Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. 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

2. If $\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}$ and Aij is cofactor of aij, then value of $\triangle$ is given by

(a)

a11 A31 + a12 A32 + a13 A33

(b)

a11 A11 + a12 A21 + a13 A31

(c)

a21 A11 + a22 A12 + a23 A13

(d)

a11 A11 + a21 A21 + a31 A31

3. If $\begin{vmatrix} x & 2 \\ 8 &5 \end{vmatrix}=0$ then the value of x is

(a)

${{-5}\over{6}}$

(b)

${{5}\over{6}}$

(c)

${{-16}\over{5}}$

(d)

${{16}\over{5}}$

4. If $\begin{vmatrix} 4 & 3 \\ 3 & 1 \end{vmatrix}=-5$ then value of $\begin{vmatrix} 20 & 15 \\ 15 & 5 \end{vmatrix}$ is

(a)

-5

(b)

-125

(c)

-25

(d)

0

5. If any three-rows or columns of a determinant are identical, then the value of the determinant is

(a)

0

(b)

2

(c)

1

(d)

3

6. 3 x 2 = 6
7. Show that $\left[ \begin{matrix} 8 & 2 \\ 4 & 3 \end{matrix} \right]$is non – singular.

8. Find adj A for $A=\left[ \begin{matrix} 2 & 3 \\ 1 & 4 \end{matrix} \right]$

9. If $A=\left| \begin{matrix} -2 & 6 \\ 3 & -9 \end{matrix} \right|$then, find A-1

10. 3 x 3 = 9
11. Evaluate$\left| \begin{matrix} 1 & a & { a }^{ 2 } \\ 1 & b & { b }^{ 2 } \\ 1 & c & { c }^{ 2 } \end{matrix} \right|$= (a–b) (b–c) (c–a)

12. If $A=\left[ \begin{matrix} 2 & 4 \\ -3 & 2 \end{matrix} \right]$then, find A -1.

13. The technology matrix of an economic system of two industries is $\left[ \begin{matrix} 0.8 & 0.2 \\ 0.9 & 0.7 \end{matrix} \right]$ Test whether the system is viable as per Hawkins – Simon conditions.

14. 2 x 5 = 10
15. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs.320. The cost of 2kg onion, 4 kg wheat and 6 kg rice is Rs.560. The cost of 6 kg onion, 2 kg wheat and 3 kg rice is `380. Find the cost of each item per kg by matrix inversion method.

16. An economy produces only coal and steel. These two commodities serve as intermediate inputs in each other’s production. 0.4 tonne of steel and 0.7 tonne of coal are needed to produce a tonne of steel. Similarly 0.1 tonne of steel and 0.6 tonne of coal are required to produce a tonne of coal. No capital inputs are needed. Do you think that the system is viable? 2 and 5 labour days are required to produce a tonne s of coal and steel respectively. If economy needs 100 tonnes of coal and 50 tonnes of steel, calculate the gross output of the two commodities and the total labour days required.