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kingwinner
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1) True or False? If true, prove it. If false, prove that it is false or give a counterexample.
1a) If a linear transformation T: R^n->R^m is onto and R^n = span{X1,...,Xk}, then R^m = span{T(X1),...,T(Xk)}
1b) If T: R^n->R^m is a linear transformation and U is a subspace of R^n, then T(U) is a subspace of R^m.
2) Let T: R^2->R^4 be a linear transformation induced by the matrix A=
[1 4
2 3
3 2
4 1]
Find a vector X E R^2 such that T(X) is as close as possible to [4 6 6 4]^T
I have an exam tomorrow. These are the past exams questions that I am having terrible trouble with. Can someone help me? I seriously thought about these questions, but still can't come up with any clue...I really want to provide some attempt, but I don't even know how to begin...
Any help/hints is greatly appreciated!
1a) If a linear transformation T: R^n->R^m is onto and R^n = span{X1,...,Xk}, then R^m = span{T(X1),...,T(Xk)}
1b) If T: R^n->R^m is a linear transformation and U is a subspace of R^n, then T(U) is a subspace of R^m.
2) Let T: R^2->R^4 be a linear transformation induced by the matrix A=
[1 4
2 3
3 2
4 1]
Find a vector X E R^2 such that T(X) is as close as possible to [4 6 6 4]^T
I have an exam tomorrow. These are the past exams questions that I am having terrible trouble with. Can someone help me? I seriously thought about these questions, but still can't come up with any clue...I really want to provide some attempt, but I don't even know how to begin...
Any help/hints is greatly appreciated!