List of practice Questions

Solve the equation|x+a x x x x+a x x x x+a|=0,a≠0
Prove that|a2 bc ac+c2 a2+ab b2 ac ab b2+bc c2|=4a2b2c2
Let A=[1-21 -231 115]verify that
(i)[adjA]-1=adj(A-1)
(ii)(A-1)-1=A

Verify A(adj A)=(adj A)A=IAII. \(\begin{bmatrix}2&3\\-4&-6\end{bmatrix}\)

Find adjoint of each of the matrices \(\begin{bmatrix}1&-1&2\\2&3&5\\-2&0&1\end{bmatrix}\)

Find the values of k so that the function f is continuous at the indicated point.
f(x)={kx+1,if x≤5
3x-5,if x>5   at x=5

Discuss the continuity of the function f, where f is defined by

\[f(n) =   \begin{cases}     3,       & \quad \text{if } {0\leq x\leq 1}\\     4,  & \quad \text{if } {1<x<3} \\ 5,  & \quad \text{if } {3\leq x \leq 10}  \end{cases}\]

Is the function defined by

\[f(x) =   \begin{cases}     x+5,       & \quad \text{if } x{\leq 1}\\    x-5,  & \quad \text{if } x \text{>1}   \end{cases}\]

a continuous function?         

If A=\(\begin{bmatrix}2&3&5\\3&2&-4\\1&1&-2\end{bmatrix}\),find A-1.UsingA-1 solve the system of equations
2x-3y+5z=11
3x+2y-4z=-5
x+y-2z=-3

Find all points of discontinuity of f, where f is defined by 

\[f(x) =   \begin{cases}    x^{10}-1,     & \quad \text{if } x{\leq 1}\\     x^2,  & \quad \text{if } x \text{>1}   \end{cases}\]

Find all points of discontinuity of f, where f is defined by 

\[f(n) =   \begin{cases}     x^3-3,       & \quad \text{if } x {\leq 2}\\     x^2+1,  & \quad \text{if } x \text{>2}   \end{cases}\]

Solve system of linear equations, using matrix method.
 2x+3y+3z=5
 x-2y+z=-4
 3x-y-2z=3

Find all points of discontinuity of f, where f is defined by 

\[f(x) =   \begin{cases}     x+1,       & \quad \text{if } x{\geq1}\\    x^2+1,  & \quad \text{if } x \text{<1}   \end{cases}\]

Solve system of linear equations, using matrix method.
x-y+z=4
2x+y-3z=0 
x+y+z=2

Find all points of discontinuity of f,where f is defined by 

\[f(x) =   \begin{cases}     \frac {x}{|x|},       & \quad \text{if } x \text{<0}\\     -1,  & \quad \text{if } x {\geq 0}   \end{cases}\]

Solve system of linear equations, using matrix method.
2x+y+z=1
x-2y-z=\(\frac{3}{2}\)
3y-5z=9

Find all points of discontinuity of f,where f is defined by 

\[f(x) =   \begin{cases}    \frac {|x|} {x},      & \quad \text{if } x { \neq 0}\\     0,  & \quad \text{if } x { =0}   \end{cases}\]
Appearance of male secondary characters in females is

Find all points of discontinuity of f,where f is defined by 

\[f(x) =   \begin{cases}     |x|+3,      & \quad \text{if } x\  {\leq-3}\\     -2,  & \quad \text{if } -3<x<3 \text{} \\ 6x+2, & \quad \text{if } x\  {\geq 3}  \end{cases}\]

Find all points of discontinuity of f, where f is defined by 

\[f(x) =   \begin{cases}     2x+3,      & \quad \text{if } x {\leq 2}\\     2x-3,  & \quad \text{if } x \text{>2}   \end{cases}\]

Solve system of linear equations, using matrix method.
 5x+2y=3
 3x+2y=5

Solve system of linear equations, using matrix method.
4x-3y=3
3x-5y=7

Is the function f defined by

\[f(x) =   \begin{cases}     x,      & \quad \text{if } n{\leq1}\\    5,  & \quad \text{if } n{ >1}   \end{cases}\]

continuous at x=0? At x=1? At x=2?

Prove that the function f(x) = xn, is continuous at x = n, where n is a positive integer.

Solve system of linear equations, using matrix method.
  2x-y=-2
  3x+4y=3