Question

For each of the following linear operators T on vector space V, compute the determinant T...

For each of the following linear operators T on vector space V, compute the determinant T and the characteristic polynomial of T.

(a). V = R2 , T(a, b) = (2a - b, 5a + 3b)

(b). V = R3 , T(a, b, c) = (a - 3b + 2c, -2a + b + c, 4a - c)

(c). V = P3(R) , T(a, b, c) = T(a + bx + cx2 + dx3) = (a - c) + (-a + b + d)x + (a + b - d)x2 - cx3

(d). V = M2x2 (R) , T(A) = 2AT - A

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