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**Homework Statement**

Write the vector (1,2,3) as a linear combination of the vectors (1,0,1), (1,0,-1), and (0,1,1).

**The attempt at a solution**

(1,2,3) = C1(1,0,1) + C2(1,0,-1) + C3(0,1,1)

The matrix for this is:

[tex]1....1....0....1[/tex]

[tex]0....0....1....2[/tex]

[tex]1....-1....1....3[/tex]

I reduced it to the following:

[tex]1....0....0....1[/tex]

[tex]0....1....0....0[/tex]

[tex]0....0....1....2[/tex]

Therefore, (1,2,3) is a linear combination of the vectors (1,0,1), (1,0,-1), and (0,1,1). Am I right?

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