Reduce each of the following matrix to normal form and hence find their rank

\(\begin{bmatrix}2&3&-1&-1\\1&-1&-2&-4\\3&1&3&-2\\6&3&0&-7\end{bmatrix}\)

Find the rank of matrix

\(\begin{bmatrix}8&1&3&6\\0&3&2&2\\-8&-1&-3&4\end{bmatrix}\)

For the matrix 

\(A=\begin{bmatrix}1&1&2\\1&2&3\\0&-1&-1\end{bmatrix}\)

For non singular matrices P and Q such that PAQ is in the normal form. Hence find the rank of A.

Reduce to triangular form

\(\begin{bmatrix}3&-4&-5\\-9&1&4\\-5&3&1\end{bmatrix}\)

Use Gauss-jordan method to find the inverse of matrix\(\begin{bmatrix}8&4&3\\2&1&1\\1&2&1\end{bmatrix}\)

Solve thehelp of matrix the simultaneous equations :

\(x+y+z=3, x+2y+3z=4, x+4y+9z=6\)

Solve the system of equations

\(2x_{1}+x_{2}+2x_{3}+x_{4}=6\)

\(4x_{1}+3x_{2}+3x_{3}-3x_{4}=-1\)

\(6x_{1}-6x_{2}+6x_{3}+12x_{4}=36\)

\(2x_{1}+2x_{2}-x_{3}+x_{4}=10\)

Using matrix mathod , show that the equations

3x+3y+2z=1,

x+2y=4,

10y+3z=-2,

2x-3y-z=5

are consistent and hence obtain the solution for x,y,and z.

For what value of the parameter \(\lambda ,\mu\)do the system of equations

1) no solution 

2) unique solution

3) more than one solution

\(x+y+z=6,x+2y+3z=10,x+2y+\lambda{z}=\mu\)

A, B and C can do a piece of work in 20, 30 and 60 days respectively. 
In how many days can A do the work if he is assisted by B and C on every third day?

A : 12days
B : 15days
C : 16days
D : 18days

Find the value of integration:

\(\int{(3X+5)^{3}}dx\)