[" 37."x-y+z=4],[x-2y-2z=9],[2x+y+3z=1]

x+y+z=4 2x-y+z=-1 2x+y-3z=-9

Solve the following system of equations: x-y+z=4,\ \ \ \ x-2y-2z=9,\ \ \ \ 2x+y+3z=1

Solve x-y+z=4 , x+y+z=2 , 2x+y-3z=0

2x-y+z=6,x+2y+3z=3,3x+y-z=4

x-y+z=1 2x+y-z=2 x-2y-z=4

Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z-x)dot

x+2y-2z=5,3x-y+z=8,x+y-z=4

Show that each of the following systems of linear equations is consistent and also find their solutions: 6x+4y=2 9x+6y=3 2x+3y=5 6x+9y=15 5x+3y+7z=4 3x+26 y+2z=9 7x+2y+10 z=5 x-y+z=3 2x+y-z=2 -x-2y+2z=1 x+y+z=6 x+2y+3z=14 x+4y+7z=30 2x+2y-2z=1 4x+4y-z=2 6x+6y+2z=3

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)