Suppose A and B is are ntimesn matrices det A 23 and det B

Suppose A and B is are ntimesn matrices, det A = 2/3, and det B = 2/5. The linear transformation T: P_3 rightarrow P_3 is defined by Let T be the linear transformation given in problem 11. Determine whether there is a function h(x) epsilon P_3 so that T(h(x)) = 3x^2 - 4x + 1. If there is no such function, then enter 999. If there are infinitely many solutions then enter 888. Otherwise, give the value for h(1).

Solution

8. As per determinant property: det A^-1 = 1/detA

  det A^-1 = 1/ 2/3 = 3/2

9. As per determinant property:   detA^T = detA = 2/3

10. As per determinant property:   detA.B = detA*detB = (2/3)*(2/5) = 4/15