[" 3.If "([x+3,2y+x],[z-1,4a-z])=[[0,-7],[3,2a]]" then "],[x+y+z+a=],[1)-1," 2) "0," 3) "1]

[[2,5],[3,4]][[3,1],[-2,3]]=[[x,y],[1,z]] find x,y and z.

Prove that |[x,y,z] , [x^2, y^2, z^2] , [yz, zx, xy]| = |[1,1,1] , [x^2, y^2, z^2] , [x^3, y^3, z^3]|

if 3x-4y+2z= -1, 2x+3y+5z=7, x+z=2, then x=

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

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

The determinant |[ C(x,1) ,C(x,2), C(x,3)] , [C(y,1) ,C(y,2), C(y,3)] , [C(z,1) ,C(z,2), C(z,3)]|= (i) 1/3xyz(x+y)(y+z)(z+x) (ii) 1/4xyz(x+y-z)(y+z-x) (iii) 1/12xyz(x-y)(y-z)(z-x) (iv) none

The determinant |[ C(x,1) ,C(x,2), C(x,3)] , [C(y,1) ,C(y,2), C(y,3)] , [C(z,1) ,C(z,2), C(z,3)]|= (i) 1/3xyz(x+y)(y+z)(z+x) (ii) 1/4xyz(x+y-z)(y+z-x) (iii) 1/12xyz(x-y)(y-z)(z-x) (iv) none

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

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