#### Matrices And Determinants Two Marks Question

11th Standard

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Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. 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.

2. Find the minors and cofactors of all the elements of the following determinants
$\begin{vmatrix}5&20\\ 0&-1 \end{vmatrix}$

3. Solve: $\begin{vmatrix}2& x&3\\4&1&6\\1&2&7 \end{vmatrix}=0$

4. Find |AB| if $A=\begin{bmatrix} 3&-1\\2&1 \end{bmatrix}and \begin{bmatrix} 3&0\\1&-2 \end{bmatrix}$

5. If A $=\begin{bmatrix} 1 \\ -4\\3 \end{bmatrix}$ and  B = [-1 2 1], verify that (AB)T = BT. AT.

6. Evaluate $\begin{vmatrix} 2 &-1 &-2 \\0 & 2 & -1\\3 & -5& 0 \end{vmatrix}.$

7. Find the values of x if $\begin{vmatrix} 2 & 4 \\5 & 1 \end{vmatrix}=\begin{vmatrix} 2x & 4\\6 & x \end{vmatrix}.$

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

9. Using the property of determinants show that $\begin{vmatrix} x &a &x+a \\ y & b &y+b \\z & c & z+c \end{vmatrix}=0.$

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

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

12. Show that$\left| \overset { x }{ 2x\underset { a }{ + } 2a } \quad \overset { y }{ 2y\underset { b }{ + } 2b } \quad \overset { z }{ 2z\underset { c }{ + } 2c } \right| =0$

13. Solve$\left| \begin{matrix} x-1 & x & x-2 \\ 0 & x-2 & x-3 \\ 0 & 0 & x-3 \end{matrix} \right| =0$

14. Show that $\left[ \begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix} \right]$is a singular matrix.

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