Let A= ( array c 0 -6 8 array ), B= ( array ccc 3 & 5 & -7 0 & -1 & 8 6 & -1 & 0 array ) and X= ( array l x y z array ) . If D =[ ]^ T is the solution of X ^ T B ^ T = A ^ T , then D ^ T A =

Step-by-step solution

aligned & X^T B^T=A^T & (X^T B^T )=A^T B X=A & |B|= | array ccc 3 & 5 & -7 0 & -1 & 8 6 & -1 & 0 array |=222, B⁻¹= 1 222 | array lll 8 & 7 & 33 48 & 42 & -24 6 & 33 & -3 array | & X=B⁻¹ A= 1 222 [ array lll 8 & 7 & 33 48 & 42 & -24 6 & 33 & -3 array ] [ array l 0 -6 8 array ] & [ array l x y z array ]= 1 222 [ array c 222 -444 -222 array ]= [ array c 1 -2 -1 array ]=D= [ array l array ] & Now, D^T A= [ array lll 1 & -2 & -1 array ] [ array c 0 -6 8 array ]=[0+12-8]=4 & aligned