# Find a basis

I don't wan't a solution I wan't only instructions how to solve this problem:

Find a basis for the span: $$\vec{a_{1}}=(1,\,-1,\,6,\,0),\,\vec{a_{2}}=(3,\,-2,\,1,\,4),\,\vec{a_{3}}=(1,\,-2,\,1,\,-2),\,\vec{a_{4}}=(10,\,1,\,7,\,3)$$

Make a matrix with a1, a2, a3, and a4 in separate rows, with each component of each vector in a separate column. Put it in row reduced echelon form. The nonzero rows of your new matrix are the vectors that form the basis.

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So under your guidance the row reduced eshelon form of the matrix:

$$A=\left( \begin{array}{cccc}1 &-1 & 6 & 0\\ 3 &-2 & 1 & 4\\ 1 &-2 & 1 &-2\\ 10 & 1 & 7 & 3\\ \end{array} \right)$$ is $$\left( \begin{array}{cccc}1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1\\ \end{array} \right)$$ so the basis are vectors $$\vec{e_1}(1,\,0,\,0,\,0),\,\vec{e_2}(0,\,1,\,0,\,0),\,\vec{e_3}(0,\,0,\,1,\,0)$$ and $$\vec{e_4}(0,\,0,\,0,\,1)$$ right?

yeah that's what I got

Thanks a lot for the tips :).

HallsofIvy
Which says that the span of those four vectors is, in fact, all of $R^4$.