[" If "A=[[2,0,0],[0,2,0],[0,0,2]]" and "B=[[x_(1),y_(1),z_(1)],[x_(2),y_(2),z_(2)],[x_(3),y_(3),z_(3)]]." Prove that "],[AB,=2B.]

A=[[2,0,00,2,00,0,2]] and B=[[x_(1),y_(1),z_(1)x_(2),y_(2),z_(2)x_(3),y_(3),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)

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

If A=[[x,2,3],[-1,5,3]] , B=[[1,-2,y],[1,z,-2]] and C=[[3,0,1],[0,2,1]] , also A+B-C=O then find x,y,z

If A=[[x,2,3],[-1,5,3]] , B=[[1,-2,y],[1,z,-2]] and C=[[3,0,1],[0,2,1]] , also A+B-C=O then find x,y,z

If A=[[x,2,3],[-1,5,3]] , B=[[1,-2,y],[1,z,-2]] and C=[[3,0,1],[0,2,1]] , also A+B-C=O then find x,y,z

Suppose the system of equations a_(1)x+b_(1)y+c_(1)z=d_(1) a_(2)x+b_(2)y+c_(2)z=d_(2) a_(3)x+b_(3)y+c_(3)z=d_(3) has a unique solution (x_(0),y_(0),z_(0)) . If x_(0) = 0 , then which one of the following is correct ?

For x_(1), x_(2), y_(1), y_(2) in R if 0 lt x_(1)lt x_(2)lt y_(1) = y_(2) and z_(1) = x_(1) + i y_(1), z_(2) = x_(2)+ iy_(2) and z_(3) = (z_(1) + z_(2))//2, then z_(1) , z_(2) , z_(3) satisfy :