Solve the system of equations $\frac{2}{x} + \frac{3}{y} + \frac{10}{z} = 4$, $\frac{4}{x} - \frac{6}{y} + \frac{5}{z} = 1$, $\frac{6}{x} + \frac{9}{y} - \frac{20}{z} = 2$
8.
Find values of $x$, if (i) $\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix} = \begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$
9.
Solve the system of linear equations, using matrix method: $5x + 2y = 3$, $3x + 2y = 5$
10.
Verify $A (adj A) = (adj A) A = |A| I$ for the matrix $\begin{bmatrix} 2 & 3 \\ -4 & -6 \end{bmatrix}$
11.
Let $A$ be a nonsingular square matrix of order $3 \times 3$. Then $|adj A|$ is equal to
a.
$|A|$
b.
$|A|^2$
c.
$|A|^3$
d.
$3|A|$
12.
If A = $\begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix}$, then show that $| 2A | = 4 | A |$
13.
If $A$ is an invertible matrix of order 2, then det $(A^{-1})$ is equal to
a.
det (A)
b.
$\frac{1}{\det(A)}$
c.
1
d.
0
14.
Solve the system of linear equations, using matrix method: $4x – 3y = 3$, $3x – 5y = 7$
15.
Evaluate $\begin{vmatrix} 1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y \end{vmatrix}$
16.
Verify $A (adj A) = (adj A) A = |A| I$ for the matrix $\begin{bmatrix} 1 & -1 & 2 \\ 3 & 0 & -2 \\ 1 & 0 & 3 \end{bmatrix}$
17.
(ii) Find equation of line joining $(3, 1)$ and $(9, 3)$ using determinants.
18.
Evaluate the determinant: (ii) $\begin{vmatrix} x^2 - x + 1 & x - 1 \\ x + 1 & x + 1 \end{vmatrix}$
19.
The cost of 4 kg onion, 3 kg wheat and 2 kg rice is ` 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is ` 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is ` 70. Find cost of each item per kg by matrix method.
20.
Write Minors and Cofactors of the elements of following determinant: (i) $\begin{vmatrix} 2 & -4 \\ 0 & 3 \end{vmatrix}$
