[15 -3] Let V=M2×2 be the vector space of 2 × 2 matrices and let L: V →V be defined by L(X) spanning set for the image. = 20 X. Hint: The image of a spanning set is a -4] 5 -3 3 = { { a. Find L( b. Find a basis for ker(L): 189.189) ► c. Find a basis for im(L): (88.88 } } Let T P3 P3 be the linear transformation such that : T(2x²) = 2x² - 4x, T(0.5x + 3) = 3x² + 2x - 2, T(2x² + 1) = −2x − 3. Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²) = = T(ax² + bx + c) =