If `x(1,2,0)+ y(0,3,1)+z(-1,0,1) =(2,1,0)` then find `x,y,z`

If A=((-1, 2, 0), (-1, 1, 1), (0, 1, 0)) , find A^(-1) . Use it to solve the system of equations: -x+2y=2, -x+y +z=1, y+2=0 .

If [(1,0,0),(0, 0, 1),(0,1,0)][(x),(y),(z)]=[(2),(-1),(3)] , find x ,\ y ,\ z .

If [(1,0,0 ), (0,-1,0), (0,0, -1)][(x),(y),( z)]=[(1),(0),(1)] , find x ,\ y\ a n d\ z .

If [(1, 0 ,0 ),(0,y,0),( 0, 0, 1)][(x),(-1),(z)]=[(1),( 0),( 1)] , find x ,\ y\ a n d\ z .

If [(1 ,0, 0) ,(0 ,1, 0),( 0 ,0 ,1)][(x),( y),( z)]=[(1),(-1),( 0)] , find x ,\ y\ a n d\ z .

If [{:(,x-y,1,z),(,2x-y,0,w):}]=[{:(,-1,1,4),(,0,0,5):}], "find x,y,z,w"

If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,2),B(-1,2,1) and C(1,2,1), then the locus of point D is a. x+y-z=3 b. y+z=6 c. y+z=0 d. y+z=-3

If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,2),B(-1,2,1)a n dC(1,2,1), then the locus of point D is a. x+y-z=3 b. y+z=6 c. y+z=0 d. y+z=-3

STATEMENT-1 : The centroid of a tetrahedron with vertices (0, 0,0), (4, 0, 0), (0, -8, 0), (0, 0, 12)is (1, -2, 3). and STATEMENT-2 : The centroid of a triangle with vertices (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_(3), z_(3)) is ((x_(1)+x_(2)+x_(3))/3, (y_(1)+y_(2)+y_(3))/3, (z_(1)+z_(2)+z_(3))/3)

If [(x-y ,z),(2x-y,omega)]=[(-1 ,4),( 0 ,5)] , find x ,\ y ,\ z ,\ omega .