MATH 310 Quiz: Math 310 Quiz 7
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Name: find a basis for the subspace spanned by the following vectors. v1 = . The span of these vectors is the same as the column space of the matrix we get when we assemble all the vectors into a matrix. To nd a basis, we need to gure out which ones are the pivot columns. That"s echelon form; to nd the pivots, we don"t need to got all the way to rref. In this case, the pivots are the rst and second columns. So our basis is the rst and second columns of the original matrix, i. e. the vectors v1 and v2: There are two vectors in the basis: that means that the space is two-dimensional: find a basis for the nullspace of the matrix. We need to nd the general solution to ax = 0. (cid:20) 1 2 1 0. 4 0 (cid:21) (cid:20) 1 0 9 0.
