2. Let T : P2 –→ P2 be defined by T(a + bx + cx²) = a – 26 + (2b – 4c)x + 3 cx?. Find a basis C for P2 such that [T]c_is a diagonal matrix.

Consider the following two ordered bases of R3: {(2, –1, –1), (-2, 2, 1), (5, –3, –2)}, {(0, 1, 1), (0,0, 1), (1, 0, – 1)}. B | 6. C a. Find the change of basis matrix from the basis B to the basis C. [id]% b. Find the change of basis matrix from the basis C to the basis B. [id]

Let H:R* → R2 be defined by H(x1, x2, X3, X4) = (x3 + x4, X1). Find the standard matrix for H. (H is linear and no need to verify) 9.

Let A be an n × n matrix over C, then det(A¯) = det(A), where A¯i,j = Ai,j .Here, z¯ = a − ib when z = a + ib, the complex conjugate of z.