Let S = {uj, uz} be the basis for R?, where u = (1,1) and uz = (1,0) and T: R2 → R? are linear transformations where: T|u| = (1,–2) and T|uz| = (-4,1), find: a. formula for T(x1, x2) b. value of T(5,-3)

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Q: Q3. a) Express the vector (4,2) e R' as linear combination of the vectors (1,1) and (1,-1). b) Let T…

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Q: Let T: R? R² be a linear transformation that sends the vector u = (5, 2) into (2, 1) and maps v =…

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Q: Let Let T: R² R2 be the linear transformation satisfying Find the image of an arbitrary vector…

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Q: ) Let T : R? → R? be a linear transformation that sends the vector u = (5,2) into (2, 1) and maps i…

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Q: V= Let T: R² R2 be a linear transformation that sends the vector u = (5,2) into (2, 1) and maps =…

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Q: Q.3. Let R, (x) be a reflection of any vector x through the line along the vector u and P, (x) be a…

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A: Given: T(x,y) = (x-2y, -x+3y, 3x - 2y) T(x) = (-1, 4, 9) To find: The vector x = (x1, x2)

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Q: Let the linear transformation T : R² → R² be such that T(1, 1) = (1, –2), T(-1,1) = (-4, 1) Find a…

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Q: Let e1= (1,0) e2=(0,1), x1=(1,6) and x2=(4,−5) Let T: R2→R2 be a linear transformation that sends…

A: Given e1=(1,0), e2=(0,1)x1=(1,6), x2=(4,-5)   T maps e1→x1  and e2→x2. The objective is to find…