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Take an `m` by `n` matrix `A` . Let vector `b` be a vector in `R^m` . Assume that...
Take an `m` by `n` matrix `A` . Let vector `b` be a vector in `R^m` . Assume that
vector `x = <a_1,...,a_n>`
is a solution for the matrix equation `Ax=b`. Show that vector `b` is in the column space of `A` by writing vector `b` as a linear combination of the columns of `A.`
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High School Teacher
Let `A_1,A_2,ldots,A_n` be columns of matrix `A.` Now we have
Hence we can write vector `b` as
which is a linear combination of columns of `A`. Thus `b` is in the column space of `A.`
Posted by tiburtius on April 16, 2013 at 5:31 AM (Answer #1)
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