Consider linear transformation T: P₁ → P₁ given by T(x¹) = 5x¹+3x²³, T(x³) = −4x¹ + (−5)x³, T(2²)=-3x¹ + -2x² +-2x, T(x¹) = 5x¹ +5x³ + 5x² + 2x, and T(1) ·0x4 + 0x³ + (0)x² + 3x + 3. For each of the following subspaces, answer "1" if it is T-invariant and "0" otherwise. The subspace of P₁ with ordered basis {224 +22³ + 2x² + 2x +2}. 0 The subspace of P₁ with ordered basis {24, z¹+z³}. The subspace of P₁ with ordered basis {2z4+2x³ + x², -2¹-x³+x²}.

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Q: T(x¹) = 5x¹ + 3x³, T(x³) = −4x¹ + (-5)x³, T(x²)=-3x² + -2x² +-2x, T(x¹) = 5x¹ + 5x³ + 5x² + 2x, and…

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A: This is a linear algebra question. The standard matrix is find with respect to the standard basis.

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