Consider the vectors В , ūz , ūz Let T : R3 → R³ be the linear transformation defined by T(ciũi + czủ2 + czu3) = (c1 + c2 + c3)ũ1 + (2c1 + c3)ủ2 – (2c2 + c3)ūz. a) Find a matrix representation of T with respect to the basis B. b) Write the vector (7,5, 2)" as a linear combination of the elements in B. c) Determine T(7,5, 2).

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Q: Find the basis for the orthogonal complement V: v1=(1,-3,3,5) v2=(2,-5,9,3)

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Q: Determine whether the set of vectors {(2,-1,3),(4,1,2),(8,-1,8)} form a basis for R3.

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Q: Project the vector b = (1,3,1)" onto the line through %3D a13D (-1,2, 2)Т, (2, 2, –1)", аz 3D az=…

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Q: V is a 3-dimensional vector space with basis B = (vı, V2, v3). Let w = vi + v2 + v3, w2 = v2+V3, W3…

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