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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}.

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}.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider linear transformation T: P₁ → P₁ given by T(x¹) = 5x¹ + 3x³, T(1³) = −4x¹ + (−5)x³, T(x²) = −3x¹ + -21² +-21, T(x¹) = 5x¹ + 5x³ + 5x² + 2x, and T(1) = 0z¹+0z³ + (0)x² + 3x + 3. For each of the following subspaces, answer "1" if it is T-invariant and "0" otherwise. The subspace of P4 with ordered basis {2x¹ +22³ + 2x² + 2x +2}. 0 The subspace of P₁ with ordered basis {x¹, x¹ + x³}. The subspace of P with ordered basis {2x4+2x³+x², -¹- x³ + x²}. 1 The subspace of P4 with ordered basis {2x4+2r³+x²+x+1, x²+x+1, 3r¹+1²+x+1}. 0 The subspace of P with ordered basis {4, x¹+x³+x²+x}. The subspace of P₁ with ordered basis {x¹, x²¹+x³, x² + x³ + x², 1 x¹ + x³ + x² + x, x¹+x³+x²+x+1}. Let U denote the 2-dimensional T-invariant subspace from above, and let B denote the given ordered basis. Using Tu to denote the restriction of T to U₁ Mg(T|u)=
Transcribed Image Text:Consider linear transformation T: P₁ → P₁ given by T(x¹) = 5x¹ + 3x³, T(1³) = −4x¹ + (−5)x³, T(x²) = −3x¹ + -21² +-21, T(x¹) = 5x¹ + 5x³ + 5x² + 2x, and T(1) = 0z¹+0z³ + (0)x² + 3x + 3. For each of the following subspaces, answer "1" if it is T-invariant and "0" otherwise. The subspace of P4 with ordered basis {2x¹ +22³ + 2x² + 2x +2}. 0 The subspace of P₁ with ordered basis {x¹, x¹ + x³}. The subspace of P with ordered basis {2x4+2x³+x², -¹- x³ + x²}. 1 The subspace of P4 with ordered basis {2x4+2r³+x²+x+1, x²+x+1, 3r¹+1²+x+1}. 0 The subspace of P with ordered basis {4, x¹+x³+x²+x}. The subspace of P₁ with ordered basis {x¹, x²¹+x³, x² + x³ + x², 1 x¹ + x³ + x² + x, x¹+x³+x²+x+1}. Let U denote the 2-dimensional T-invariant subspace from above, and let B denote the given ordered basis. Using Tu to denote the restriction of T to U₁ Mg(T|u)=
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