Let A = {(1,1), (0, –1)} and B = {x, 1} bases of R² and P, and the linear transformation T:R? → P, where P is the vector space of polynomials of degree less than or equal to one, such that MA(T) = ( ) a) Obtain the correspondence rule of the transformation T. b) Obtain the correspondence rule, if it exists, of T-1.

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A: Here we can use the composition of function formula to find the required values.

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A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: Let V be a vector space, v, u € V, and let T₁ : V → V and T₂ : V → V be linear transformations such…

A: Here we can use the composition of function formula to find the required values.

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Q: -5 -4 40-0 and b -5 5 -4 20 -17 18 81 Define the linear transformation T: R³ → Rª by T(x) = Ax. Find…

A: Given matrix

Q: Prove that v5 is irrational.

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Q: Consider the ordered bases B₁ = {(−1, 1, 0), (0, 1, 1), (1, 0, 0)} of R³ and B₂ = {(1, 2), (1, −1)}…

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A: we have to  prove that T is a linear transformation .Then have to determine whether T is a

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A: The null space of T is the collection of all polynomials p(x) in the domain of T such that T(p(x)) =…

Q: Let E= {e,, e2, e3} be the standard basis for R°, B= (b, , b2, b3} be a basis for a vector space V,…

A: The solution is given below