Let a = {a, a2} = {x,1+x} and B = {B, B} = {x + x,...

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Let a = {a₁, a2} = {x,1+x} and B = {B₁, B₂} = {x² + x, 2x}. Let J be the transformation from the first question. (i) Write J(a₁) as a linear combination of B₁ and ₂. (ii) Write J(a₂) as a linear combination of B₁ and ₂. Show your work and explain each step. Q1 (2 points) Let J: P₁ (R) → W where WC P₂ (R) and where J is the integration operator such that J(p) = [p(x) dx with the constant term of the anti-derivative equal to zero. In other words, J(p) (0) = 0. This is another way of writing J(p) = 0 when x = 0. Write a general formula for J (p) for an arbitrary polynomial p = P₁ (R). Q3 (4 points) Let a = {a₁, a₂} = {x,1+x} and B = {B1, B₂} = {x² + x, 2x}. Let J be the transformation from the first question. (i) Write J (a₁) as a linear combination of B₁ and ₂. (ii) Write J(a₂) as a linear combination of B₁ and ₂. Show your work and explain each step. Let a = {a₁, a2} = {x,1+x} and B = {B₁, B₂} = {x² + x, 2x}. Let J be the transformation from the first question. (i) Write J(a₁) as a linear combination of B₁ and ₂. (ii) Write J(a₂) as a linear combination of B₁ and ₂. Show your work and explain each step. Q1 (2 points) Let J: P₁ (R) → W where WC P₂ (R) and where J is the integration operator such that J(p) = [p(x) dx with the constant term of the anti-derivative equal to zero. In other words, J(p) (0) = 0. This is another way of writing J(p) = 0 when x = 0. Write a general formula for J (p) for an arbitrary polynomial p = P₁ (R). Q3 (4 points) Let a = {a₁, a₂} = {x,1+x} and B = {B1, B₂} = {x² + x, 2x}. Let J be the transformation from the first question. (i) Write J (a₁) as a linear combination of B₁ and ₂. (ii) Write J(a₂) as a linear combination of B₁ and ₂. Show your work and explain each step.

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