Problem set 10: Matrix Algebra 1) If A = (2 -3) and B = (31 2 ) Find a) AB, b) BA, c) A2, d) B2 4 2) If A = 5 10 and B = - 3 - 3 12 Find a) AB, b) BA 3) If A = ( ) and B = (7 2) Find a) (AB ) T, b) AT + B, C) 2A + BT 4) 3 5 2 5) Write the system of equations: 2x1 + 6x2 + X3 =7 x1 + 2x2-X3 =-1 5x1 + 7x2 -4X3 = 9 as a matrix equation AX=B, where X and B are column vectors. 6) True or False a) (A + B)2 = A2 + 2AB + B^2 b) (A + B)(A - B) = A2 - B2 ANSWERS: 1 ) a ) ( 17 - 2 2 ) , b) ( 32 27 ) , c ) (-130 31 ) , d ) ( 3 2 2 ) 0 2) a) -10 0 5 . 6) ( 3 82 ) -20 12