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## Homework Statement

find the basis of a subspace of R^3 spanned by S:

1. S = { (4,4,8) (1,1,2) (1,1,1)}

2. S = { (1,2,2) (-1,0,0) (1,1,1)

## Homework Equations

Im allowed to use calculator.

## The Attempt at a Solution

Im not really sure what this is about. . .I tried the following and got the correct answer on a previous problem. . .but this time it didnt work:

first reduce the matrix to row echelon form which on problem 1 is:

[1 1 2]

[0 0 1]

[0 0 0]

therefore its rank 2 and the basis should be (1, 1, 2) (0, 0, 1) ?

the answer in the back is (1, 1, 0) (0, 0, 1)

I have like no clue as to what to do to get there. . .

so for the second one following the same steps I get

[1 2 2]

[0 1 1]

[0 0 0]

therefore again its rank 2 and . . .well I dont know how to get the basis? trying a guess Id say its (0, 0, 1) and (1, 1, 0)

?? I mean what is that based on? could it maybe be (1, 0, 1) (0, 1, 0) also?

I already re-read the book and just dont understand it. . .

tho people recommended me to not understand linear algebra (yet) and just follow steps. . .but still how do I get there?

-thanks