Not sure really where to start Let TA:R3 rightarrow R2 be the matrix transformation associated with a matrix A, and suppose that TA(1,1,0) = (3,-7), TA(1,-1,0) = (5,9), TA( 1,1,1) = (6,-4). Find the matrix A. Solution The final matrix is equal to (2X1) Hence the matrix A must be of order 2 X 3 so when multiplied by 3X1 vector will result into 2X1 vector using the first relation we get From first relation a + b = 3 d + e = -7 From second relation a - b = 5 d - e = 9 From third relation a + b + c = 6 d + e + f = -4 We get after solving these 6 equations, the values as follows a = 4, b = -1 d = 1, e = -8 c = 3, f = 3 Hence the A matrix which is 3X2 matrix is equal toabcdef.