Let V be the vector space of 2 x 2 matrices with real entries, and P3 the vector space of real polynomials of degree 3 or less. Define the linear transformation T : V P3 by a 2a + (b – d)a- (a + c)z? + (a + b – c - d)x?. Find the rank and nullity of T.

Q: 2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B = {1+x= 2x°, -1+a…

A: given B=1+x-2x2 , -1+x+x2 , 1-x+x2B'=1-3x+x2, 1-3x-2x2 , 1-2x+3x2 b) find the coordination matrices…

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A: The answer is given by change of basis matrix and matrix multiplication as given follows :

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A: domain of dimension = 4

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A: Given :T(v1)=(1,-1,2)T(v2)=(0,3,2)T(v3)=(-3,1,2)

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A: Linear operator should satisfy L:Rn→Rn  a) Lu+v=Lu+Lv         u,v∈Rn b)Lcu)=cL(u

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A: Introduction: A linear transformation is a function from one vector space to another that maintains…

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A: Find the functional value at each basis vector and write in linear combination of vectors in basis

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A: We have

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A: Given linear transformation: L: V →V defined by L(xi) = x3-i, i = 0, 1, 2, 3 a) B = {1, x, x2, x3}.…

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A: Answer is : X = (0 0 0 0) t

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A: We can find the answer in the following steps,

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A: The solution is given below

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Q: Let P3 be the vector space of polynomials of degree 3 or less. Define T: P3 → P3 to be the linear…

A: To find the matrix representation of the given linear transformation.

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A: Note: According to bartleby we have to answer only first three subparts please upload the question…

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A: A detailed solution is given below.

Q: The matrices A1 = . A2 = A3 = Го A4 = form a basis for the linear space V = R2x2. write the matrix…

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