+1 Hi! I'm stuck on this problem. (It has three parts). I'm not sure how to turn it into LaTeX, sorry.
a) Consider the matrix\[\mathbf{A} = \begin{pmatrix} 2 & 4 \\ 1 & 2 \end{pmatrix}.\]If the columns of $\mathbf{A}$ are linearly independent, answer with $?$. If they aren't, find coefficients $a$ and $b$, not both $0$, such that \[a \begin{pmatrix} 2\\ 1 \end{pmatrix} + b \begin{pmatrix} 4 \\ 2 \end{pmatrix} = \begin{pmatrix}0 \\ 0 \end{pmatrix}\]and answer with $\dfrac{a}{b}$.
b) Consider the matrix Solve the equation
If the only solution is , answer with . If there exists another solution answer with .
c) Consider the matrix $\mathbf{A} = \begin{pmatrix} 2 & 4 \\ 1 & 2 \end{pmatrix}.$ Then what is $\mathbf{A}^{-1} \begin{pmatrix} 0 \\ 0 \end{pmatrix}?$ If this is not defined, answer with $\begin{pmatrix} ? \\ ? \end {pmatrix}.$
