Let ū = and let T : R → R’ be the transformation defined by T(3) =i x ů. 3 (a) Prove that T is linear. (b) Find the standard matrix for T. (c) Without row reducing or performing any calculations, what is the dimension of the null space of the matrix you found in part (b). Briefly justify.

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need some help with the question. Got very confused on that.

Let ủ :
2
and let T : R → R’ be the transformation defined by T(ỉ) = x x ủ.
3
(a) Prove thatT is linear.
(b) Find the standard matrix for T.
(c) Without row reducing or performing any calculations, what is the dimension of the null space of the
matrix you found in part (b). Briefly justify.
Transcribed Image Text:Let ủ : 2 and let T : R → R’ be the transformation defined by T(ỉ) = x x ủ. 3 (a) Prove thatT is linear. (b) Find the standard matrix for T. (c) Without row reducing or performing any calculations, what is the dimension of the null space of the matrix you found in part (b). Briefly justify.
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