Let `X=[{:(x_(1)),(x_(2)),(x_(3)):}],A=[{:(1,-1,2),(2,0,1),(3,2,1):}]` and `B=[{:(3),(1),(4):}]`.If AX=B, then X is equal to

If A={:((1,-3,4),(2,1,-2)):},B={:((-2,-4,5),(1,-1,3)):} and 5A-3B+2X=O, then X=

If |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=|{:(a_(1),b_(1),1),(a_(2),b_(2),1),(a_(3),b_(3),1):}| , then the two triangles with vertices (x_(1),y_(1)) , (x_(2),y_(2)) , (x_(3),y_(3)) and (a_(1),b_(1)) , (a_(2),b_(2)) , (a_(3),b_(3)) must be congruent.

Suppose the vectors x_(1), x_(2) and x_(3) are the solutions of the system of linear equations, Ax=b when the vector b on the right side is equal to b_(1), b_(2) and b_(3) respectively. If x_(1)=[(1),(1),(1)], x_(2)=[(0),(2),(1)], x_(3)=[(0),(0),(1)], b_(1)=[(1),(0),(0)], b_(2)=[(0),(2),(0)] and b_(3)=[(0),(0),(2)] , then the determinant of A is equal to :

Let x=[x_1x_2x_3],A=[1-1 2 2 0 1 3 2 1]a n dB=[3 2 1]dotIfA X=B , Then X is equal to [1 2 3] (b) [-1-2-3] (c) [-1-2-3] (d) [-1 2 3] (e) [0 2 1]

Let A=[(2, -1, 1),(-2, 3, -1),(-4, 4, -x)] be a matrix. If A^(2)=A , then the value of x is equal to

STATEMENT-1: If three points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are collinear, then |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 STATEMENT-2: If |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 then the points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) will be collinear. STATEMENT-3: If lines a_(1)x+b_(1)y+c_(1)=0,a_(2)=0and a_(3)x+b_(3)y+c_(3)=0 are concurrent then |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=0