If `[1 4 2 0]=[x y^2z0],y<0t h e nx-y+z=`

The equation [[1, 2 ,2 ],[1 ,3, 4],[ 2, 4,k]][[x ,y, z]] =[[0,0, 0]] has a solution for (x ,y ,z) besides (0,0,0)dot Then the value of k is _______.

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)

Evaluate the following: |[0,x y^2,x z^2],[x^2y,0,y z^2],[x^2z, z y^2, 0]|

If x, y, z are different and Delta=|[x, x^2, 1+x^3],[y, y^2, 1+y^3],[z, z^2, 1+z^3]|=0 then show that 1+xyz=0

If x, y, z are different and Delta=|[x, x^2, 1+x^3],[y, y^2, 1+y^3],[z, z^2, 1+z^3]|=0 then show that 1+xyz=0

Multiply each of the monomial : 3/4x^2y z^2,\ 0. 5 x y^2z^2,\ 1. 16 x^2y z^3,\ 2x y z

If [[1 1 1],[0 1 1],[0 0 1]] [[x],[y],[z]] = [[6],[3],[2]] ,then 2x+y-z=?

Use product [[1,-1, 2],[ 0, 2,-3],[ 3,-2, 4]] [[-2, 0, 1],[ 9, 2,-3],[ 6, 1,-2]] to solve the system of equation: x-y+2z=1 ; 2y-3z=1 ; 3x-2y+4z=2

If x ,\ y ,\ z are non-zero real numbers, then the inverse of the matrix A=[[x,0, 0],[ 0,y,0],[ 0, 0,z]] , is (a) [[x^(-1),0 ,0 ],[0,y^(-1),0],[ 0, 0,z^(-1)]] (b) x y z[[x^(-1),0 ,0],[ 0,y^(-1),0],[ 0, 0,z^(-1)]] (c) 1/(x y z)[[x,0, 0],[ 0,y,0],[ 0, 0,z]] (d) 1/(x y z)[[1, 0, 0],[ 0 ,1, 0],[ 0, 0, 1]]

If [[x-y, 2x+z],[2x-y,3z+omega]] =[[-1,5],[0,13]] find x+y+z+omega