What is a Key Matrix?

3x3 matrix "A", times 3x1 matrix {{X}, {Y}, {Z}}, = 3x1 matrix {{X+Y}, {X-Y}, {0}}. What is metirx "A" (in terms of X,Y, &Z)?

• ...                                                                               X                X+Y Find 3 by 3 matrix "A", such as that matrix "A" *  Y = matrix  X-Y   ?                                                                               Z                  0

• Answer:

  how about: A= [1 1 0] [1 -1 0] [0 0 0] simply imagine the stuff on the right side is three expressions: expression #1 is: 1x+1y+0z expression #2 is: 1x-1y+0z expression #3 is: 0x+0y+0z which can be expressed as the 3X3 matrix (lets call it "C") I gave you for the answer times a 3X1 column vector (lets call that one "b"): C= [1 1 0] [1 -1 0] [0 0 0] b= [x] [y] [z] so that: A dot b=C dot b and this condition is met when A=C hope that helps