Question

Linear algebra question

Answer 1

The answer is (1/3,-8/3,5/3) . I don't see how...

Answer 2

@Dido525 solve$$c_1\left(\frac23,-\frac23,\frac13\right)+c_2\left(\frac23,\frac13,-\frac23\right)+c_3\left(\frac13,\frac23,\frac23\right)=\left(-1,0,3\right)$$Comparing component by component you may find this is a system of linear equations in \(c_{1,2,3}\).

Answer 3

If all you want is that the answer actually works, let \(c_1=1/3,\,c_2=-8/3,\,c_3=5/3\) and verify.

Answer 4

I got it thanks :) . I should have closed the question :P .