- #1

- 15

- 0

Find a basis for the span: [tex]\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)[/tex]

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter ferry2
- Start date

- #1

- 15

- 0

Find a basis for the span: [tex]\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)[/tex]

- #2

- 149

- 14

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.

Last edited:

- #3

- 15

- 0

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

- #4

- 149

- 14

yeah that's what I got

- #5

- 15

- 0

Thanks a lot for the tips :).

- #6

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 969

Which says that the span of those four vectors is, in fact, all of [itex]R^4[/itex].

- #7

- 49

- 0

Share: