If X= [ array ll 3 & -4 1 & -1 array ], B= [ array cc 5 & 2 -2 & 1 array ] and A= [ array ll p & q r & s array ] satisfy the equation A X=B , then the matrix A is equal to

Step-by-step solution

X = [ array cc 3 & -4 1 & -1 array ], B = [ array cc 5 & 2 -2 & 1 array ] and A = [ array ll p & q r & s array ] Now, AX = B [ array ll p & q r & ~s array ] [ array cc 3 & -4 1 & -1 array ]= [ array cc 5 & 2 -2 & 1 array ] [ array cc 3 p+q & -4 p-q 3 r+s & -4 r-s array ]= [ array cc 5 & 2 -2 & 1 array ] aligned & 3 p+q=5 ...(i) & -4 p-q=2 ...(ii) & 3 r+s=-2 ...(iii) & -4 r-s=1...(iv) aligned From equations (i) and (ii), we get array ll & -p=7 & p=-7 q=5-3(-7) & q=26 array From equations (iii) and (iv), -r=-1 aligne