Solve tan^-1 2x + tan^-13x = \(\frac { \pi }{ 4 } \)

6

(a)

If  \(A=\left[ \begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix} \right] \) Prove that , A =\(\left[ \begin{matrix} { 3 }^{ x-1 } & { 3 }^{ x-1 } & { 3 }^{ x-1 } \\ { 3 }^{ x-1 } & { 3 }^{ x-1 } & { 3 }^{ x-1 } \\ { 3 }^{ x-1 } & { 3 }^{ x-1 } & { 3 }^{ x-1 } \end{matrix} \right] \) for every positive integer n.

6

(a)

The sum of three numbers is -1. If we multiply the second number by 2 , third number by 3 and add them we get 5. If we subtract the third number from the sum of first and second numbers we get -1. Represent it by a system of equations . Find the three numbers using inverse of a matrix

6

(a)

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)

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)