This is a general question (no specific problem): If you get abasis (any dim wil

Question

This is a general question (no specific problem): If you get abasis (any dim will do) for a solution set, whether the solutionset is Ax = B orAx = 0, what are the vectors that can be producedby the linear combinations of the basis vectors? Are they row andcolumn vectors or any combination of the elements in the matrix?For example, consider the following matrix: The basis vectors are (just assume they are correct - I copiedthem from a book): Now what vectors out of this matrix can be created by linearcombinations of V1 and V2? Any combination of elements, only rowvectors or column vectors? Thanks

Explanation / Answer

to check whether the given vectors form a basis to thesubspace of a vector space upon which a linear transformation isdefined and whose relative matrix is the given matrix , it can be reduced to echlon form which will have almost allthe rows non zero. thus, the row vectors of the matrix are linearlyindependent. so, they form a basis to a subspace spanned .

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