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)=x²-2x ✓ T(ax² + bx + c) = = Let be the plane with equation X1 ― - 3x2 - 2x3 = 0 in R³. The linear transformation T (B) - E 1 7 -107 x1 1 -2 x2 2 2 -2 x3 maps V into V so, by restricting it to V, we may regard it as a linear transformation T: V → V. Find the matrix A of the restricted map Ĩ: V → V with respect to the basis A = = [88

For the linear transformation T:R2R2 given by A=[abba] find a and b such that T(12,5)=(13,0).

1. Let Ta : ℝ2 → ℝ2 be the matrix transformation corresponding to . Find , where and .

Determine whether the function L: P2 → P2 defined by L(a0 +a1x+a2x2) = a1 +2a2xis a linear transformation. Explain, and show all your work.

Let T P3 P3 be the linear transformation such that : T(2x²) = 2x² – 4x, T(0.5x + 3) = 3x² + 2x = 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.