Question

For the following problems, use Octave/Matlab to determine whether the following sets span \(\mathbb{R}^{3}\). Remember you need to pick an arbitrary element in \(\mathbb{R}^{3}\) and see if you can write it as a linear combination of the set of vectors.

For each problem, do the following:

1) - Write the row reduced echelon matrix found by Octave.

2) - Tell me if this set spans \(\mathbb{R}^{3}\).

3) - If this set spans \(\mathbb{R}^{3}\), solve for \(\alpha, \beta, \ldots\) (in other words, tell me how to find the coefficients for the linear combination of our vectors). Otherwise, explain how can you tell the set does not span \(\mathbb{R}^{3}\)

4) - If the set spans \(\mathbb{R}^{3}\), what could you define \(\alpha, \beta, \gamma\), etc. to construct the vector \(\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]\).

a) { ( 1 0 1 ), ( 3 1 0 ), ( -1 0 0 ), ( 2 1 5 ) }

Answer 1