[x+y+z=1],[2x+3y+2z=2],[ax+ay+2az=4]

Classify the following system of equations as consistent or inconsistent: {:(x+y+z=1),(2x+3y+2z=2),(ax+ay+2ax=4):}

Examine the consistency of the system of equations x + y + z = 1 2x + 3y + 2z = 2 a x + a y + 2a z = 4

Solve the following equations by the method of inversion: x+y+z = 1 , 2x+3y+2z = 2 and ax+ay+2az = 4 .

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)

Examine the consistency of the system of equations x2x+3y+2z=2ax+ay+quad 2aquad z=4

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

The value of a such that the system of equations x-2y+z=-4, 2x – y +2z = 2 and x+y+az = 4, has no solution , is a) 0 b)1 c)3 d)-1