Let T be a linear transformation from R2 into R2 such that  T(1, 0) = (1, 1)  and  T(0, 1) = (−1, 1).  Find  T(1, 4)  and  T(1, −5).

Let T : P3 → P3 be the linear transformation such that T(-2x²) = 3x² + 3x, T(-0.5x + 3) = 3x? + 4x – 1, T(5x² + 1) = -3x + 1. Find T(1), T(x), T(x²), and T(ax? + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²) = T(ax? + bx + c) =

Let f: R²R be defined by f((x, y)) = 8y - 4x + 1. Is ƒ a linear transformation? a. f((x1, y₁) + (x2, Y2)) (Enter x₁ as x1, etc.) f((x₁, y₁)) + f((x2, y₂)) = + Does f((x1, y₁) + (x2, 2)) = f((x₁, y₁)) + f((x2, ₂)) for all (x1, y₁), (x2, Y₂) € R²? choose b. f(c(x, y)) = c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all CER and all (x, y) = R²? choose c. Is f a linear transformation? choose

Let T: R2→R? be a linear transformation such that T (x1,X2) = (xq +X2, 5x1 + 6x2) · Find x such that T(x) = (3,10). %3D X=