Find the value of :
`x^3+y^3+3xyz` given that `x=-1,y=2 and z=3`

Find the value of the following. 3x+y-z when x = 0, y = 1, z = -1

Find the value of x, If [[3x+y,-y],[2y-x,3]]=[[1,2],[-5,3]]

If x + y + z = xyz and x, y, z gt 0 , then find the value of tan^(-1) x + tan^(-1) y + tan^(-1) z

Find the values of x, y and z from the following equations:(i) [[4, 3],[x,5]]=[[y, z],[1, 5]] (ii) [[x+y,3],[ 5+z, x y]]=[[6, 3],[ 5 ,8]] (iii) [[x+y+z],[ x+z],[ y+z]]=[[9],[ 5],[ 7]]

Find the value of k so that the lines (1-x)/(3) = (y-2)/(2k) = (z-3)/(2) and (1+x)/(3k) = (y-1)/(1) = (6-z)/(7) are perpendicular to each other.

If x^(3) + y^(3) + z^(3) = 3xyz and x + y + z = 0 , find the value of : ((x+y)^(2))/(xy) + ((y+z)^(2))/(yz) + ((z+x)^(2))/(zx)

Find the maximum value of xyz when (x)/(1)+(y^2)/(4)+(z^3)/(27)=1 , where x,y,zgt 0 .

Find the nature of solution for the given system of equation: x+2y+3z=1;2x+3y+4z=3;3x+4y+5z=0

Evaluate the following. 2xyz+3xy when x = 2, y = 3, and z = 4.

Find the value of x , if [(3x+y,-y),(2y-x,3)]=[(1, 2),(-5, 3)] .