Answer to Question #70584 in Linear Algebra for Nawaz khan

Question

a) Check whether the following system of equations has a solution.
x+y+3z+w = 5
−x+y+z−5w = 7
x+2y+5z−w = 5 (6)
b) Let T : P2 → P1 be defined by
T(a+bx+cx2
) = b+c+ (a−c)x.
Check that T is a linear transformation. Find the matrix of the transformation with
respect to the ordered bases B1 = {x
2
, x
2 +x, x
2 +x+1} and B2 = {1, x}. Find the
kernel of T.