Solve each of the following systems of equations using matrix method.

$x-y=3$;

$2x+3y+4z=17$;

$y+2z=7$

Solve each of the following systems of equations using matrix method.

$4x+3y+2z=60$;

$x+2y+3z=45$;

If  $A=\left(\begin{array}{ccc}2& -3& 5\\ 3& 2& -4\\ 1& 1& -2\end{array}\right)$, find $A^{-1}$. Using $A^{-1}$, solve the following system of equations: $2x-3y+5z=11$; $3x+2y-4z=-5$; $x+y-2z=-3$.

If $A=\left(\begin{array}{ccc}2& 1& 1\\ 1& -2& -1\\ 0& 3& -5\end{array}\right)$ , find $A{ }^{-1}$. Using $A^{-1}$, solve the following system of linear equations: $2x+y+z=1$; $x-2y-z=\frac{3}{2}$; $3y-5z=9$.

If $A=\left[\begin{array}{ccc}1& -2& 0\\ 2& 1& 3\\ 0& -2& 1\end{array}\right], B=\left[\begin{array}{ccc}7& 2& -6\\ -2& 1& -3\\ -4& 2& 5\end{array}\right]$ and find $AB$. Hence, solve the system of equations: $x-2y=10$, $2x+y+3z=8$ and $-2y+z=7$.

Using matrices, solve the following system of equations:

$\frac{2}{x}-\frac{3}{y}+\frac{3}{z}=10$, $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=10$, $\frac{3}{x}-\frac{1}{y}+\frac{2}{z}=13$

Using matrices, solve the following system of equations:

$\frac{1}{x}-\frac{1}{y}+\frac{1}{z}=4$, $\frac{2}{x}+\frac{1}{y}-\frac{3}{z}=0$, $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2(x, y, z\ne 0)$

The sum of three numbers is$2$. If twice the second number is added to the sum of first and third, we get $1$. On adding the sum of second and third numbers to five times the first, we get $6$. Find the three numbers by using matrices.

The cost of $4 \mathrm{kg}$potato, $3 \mathrm{kg}$wheat and $2 \mathrm{kg}$of rice is $₹ 60$. The cost of $1 \mathrm{kg}$potato, $2 \mathrm{kg}$ wheat and $3 \mathrm{kg}$ of rice is $₹ 45$. The cost of $6 \mathrm{kg}$ potato, 2$2 \mathrm{kg}$ wheat and $3 \mathrm{kg}$ of rice is $₹ 70$. Find the cost of each item per$\mathrm{kg}$by matrix method.