# Thread: Linear combination

1. ## Linear combination

Course: Linear Algebra

Test question: Write a vector $\left$$5,2,4\right$$$ as a linear combination of the vectors $\left$$3,-1,6\right$$$, $\left$$2,4,3\right$$$, and $\left$$5,-1,2\right$$$.

My answer was $\left$$5,2,4\right$$= \frac{1}{10}\left$$3,-1,6\right$$+ \frac{38}{55}\left$$2,4,3\right$$+ \frac{73}{110}\left$$5,-1,2\right$$$.

Review question: Write $\left$$5,2,4\right$$$ as a linear combination of columns from $\begin{bmatrix}3 & 2 & 5 \\ -1 & 4 & -1 \\ 6 & 3 & 2 \end{bmatrix}$.

I get the same answer as I got before, just with column vectors. Should this be?

2. ## Re: Linear combination

Well, the vectors in the first case are the columns in the second case, so of course it's the same result.

3. ## Re: Linear combination

Originally Posted by emakarov
Well, the vectors in the first case are the columns in the second case, so of course it's the same result.
Are they the same question, just worded differently?

4. ## Re: Linear combination

Of course. There is nothing to prove here.