Originally Posted by

**Glitch** **The question:**

Determine, with reasons whether or not the matricies

$\displaystyle A_1 = \[ \left( \begin{array}{cc}

1 & 2 \\

2 & 1\end{array} \right)\]$

$\displaystyle A_2 = \[ \left( \begin{array}{cc}

0 & 1 \\

1 & 0\end{array} \right)\]$

$\displaystyle A_3 = \[ \left( \begin{array}{cc}

2 & 1 \\

2 & 1\end{array} \right)\]$

are linearly dependent.

**My attempt:**

Usually with these types of questions I'd create a large matrix and reduce to row echelon form. So I'd start by stating:

$\displaystyle \lambda_1A_1 + \lambda_2A_2 + \lambda_3A_3$ = **0**

And create a matrix from there. How do I do this when we have matrices instead of polynomials or vectors? Thanks!