If a \(\neq \)p b\(\neq \)q c\(\neq \)r  and \(\left| \begin{matrix} p & b & c \\ a & q & c \\ a & b & r \end{matrix} \right| \) = 0 find the value of \(\frac { p }{ p-a } +\frac { q }{ q-b } +\frac { r }{ r-c } \)

6

(a)

For the matrix A = \(\left[ \begin{matrix} 3 & 2 \\ 1 & 1 \end{matrix} \right] \)find the numbers a and b such that A² +aA + bI = O. Hence find A^-1.

6

(a)

Solve the equation if a \(\neq \) 0 and  \(\left| \begin{matrix} x+a & x & x \\ x & x+a & x \\ x & x & x+a \end{matrix} \right| \)

6

(a)

Using matrix method, determine whether the following system of equation is consisten or inconsistent
3x - y -2z =2
2y -z = -1
3x - 5y = 3

6

(a)