$$x + 2y + 3z = 0$$ 

Based on this information answer the questions given below.
Two $$n\times n$$ square matrices A and B are said to be similar if there exists a non-singular matrix P such that 
$$P^{-1}A  P=B$$

Let a, b and c be three real numbers satisfying [a b c] $$\begin{bmatrix}1 &9 & 7 \\8  & 2 & 7 \\ 7 & 3 & 7\end{bmatrix} = [0 0 0]$$

Find the cofactors of the elements of the following matrices :
(i) $$\begin{bmatrix} -1 & 2 \\ -3 & 4 \end{bmatrix}$$ 

(ii) $$\left[ \begin{matrix} 1 & -1 & 2 \\ -2 & 3 & 5 \\ -2 & 0 & -1 \end{matrix} \right] $$

Let system of linear equations $$\displaystyle a_{1}x+b_{1}y+c_{1}z=d_{1}a_{2}x+b_{2}y+c_{2}z=d_{2}$$ &$$\displaystyle a_{3}x+b_{3}y+c_{3}z=d_{3}$$ can be expressed in the form $$\displaystyle AX=B....(*)$$ where $$\displaystyle A=\begin{pmatrix}a_{1} &b_{1}  &c_{1} \\a_{2} &b_{2}  &c_{2} \\a_{3}  &b_{3}  &c_{3} \end{pmatrix}$$ ,$$\displaystyle B=\begin{pmatrix}d_{1}\\d_{2}\\d_{3}
\end{pmatrix}$$ $$\displaystyle X= \begin{pmatrix}x\\y\\z\end{pmatrix}$$ The above system of equations (*) is said to be consistent with unique solution if A is non singular & the values of the variables x, y, z can be determined by using the equation $$\displaystyle X= A^{-1} B $$ and if A is singular then system of equations are either consistent with infinitely many solutions or inconsistent with no solution accordingly $$\displaystyle (adj A) (B)= 0 $$ and $$\displaystyle (adj A) (B) \neq 0 $$ where (adj A) is the transpose of cofactor matrix of A Now Assume $$\displaystyle A=\begin{pmatrix}
a &1  &0 \\1  &b  &d \\1  &b  &c\end{pmatrix}$$,  $$\displaystyle B= 
\begin{pmatrix}a &1  &1 \\0  &d  &c \\f  &g  &h \end{pmatrix}$$ $$\displaystyle P=\begin{pmatrix}f\\g\\h\end{pmatrix}$$,$$\displaystyle Q=\begin{pmatrix}a^{2}\\0\\0\end{pmatrix}$$,$$\displaystyle X=\begin{pmatrix}x\\y\\z\end{pmatrix}$$