Question

Let L in R 3 be the line through the origin spanned by the vector v =   1 1 3  . Find the linear equations that define L, i.e., find a system of linear equations whose solutions are the points in L. (7) Give an example of a linear transformation from T : R 2 → R 3 with the following two properties: (a) T is not one-to-one, and (b) range(T) =      x y z   ∈ R 3 : x − y + 2z = 0    ; or explain why this is not possible. If you give an example, you must include an explanation for why your linear transformation has the desired properties.

1 (6) Let L in Rº be the line through the origin spanned by the vector v = 1 . Find 3 the linear equations that define L, i.e., find a system of linear equations whose solutions are the points in L. (7) Give an example of a linear transformation from T : R2 + R3 with the following two properties: (a) T is not one-to-one, and (b) range(T) = YER: 1-y + 2z = 0%; or explain why this is not possible. If you give an example, you must include an explanation for why your linear transformation has the desired properties. (9) Consider the folloin lant motric.

Answer 1

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