[x+y+2z=4],[x+2y+z=1],[x+y+z=2]

8x + y + 2z = 4x + 2y + z = 1x + y + z = 2

Solve the following equations by matrix method.x+y+2z=4,x+2y+z=1 and x+y+z=2

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)

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)

Prove that Det [[x + y + 2z, x, y], [z, y + z + 2x, y], [z, x, z + x + 2y]] = 2 (x + y + z) ^ 3

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

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

The values of x, y, z for the equations x-y+z=1, 2x-y=1, 3x+3y-4z=2 are

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