Math, asked by guruthakur, 1 day ago

a) Find linear transformation T:R^ 4 R^ 3 whose null space is generated by (0, 1, 2, 3) and (- 1, 2, 3, 0)
b) Prove that the subspace of R ^ 3 consisting of triplet (a, b, c) with c = 0 is a subspace of R ^ 3 which is isomorphic to R ^ 2

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Answered by Safiyasayeed

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Step-by-step explanation:

A linear transformation is uniquely specified by its action on a basis. We can extend the set of linearly independent vectors {(1,−1,1),(1,1,1)} to a basis for R3 by adjoining some vector v∈R3 to the set. The required linear transformation can then be specified by setting T(v) to be any vector in R2.

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a) Find linear transformation T:R^ 4 R^ 3 whose null space is generated by (0, 1, 2, 3) and (- 1, 2, 3, 0) b) Prove that the subspace of R ^ 3 consisting of triplet (a, b, c) with c = 0 is a subspace of R ^ 3 which is isomorphic to R ^ 2​

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a) Find linear transformation T:R^ 4 R^ 3 whose null space is generated by (0, 1, 2, 3) and (- 1, 2, 3, 0)
b) Prove that the subspace of R ^ 3 consisting of triplet (a, b, c) with c = 0 is a subspace of R ^ 3 which is isomorphic to R ^ 2