Math Challenges

Submissions for Problem #67

Find A such that the given set is Col(A)

\[ \left\lbrace\begin{pmatrix}2s+3t\\ r+s-2t\\ 4r+s\\ 3r-s-t\end{pmatrix}:r,s,t\in\mathbb{R}\right\rbrace \]

zapwai

Solution: \( \displaylines{\text{Factoring the variables out gives}\\ r\begin{pmatrix}0\\ 1\\ 4\\ 3\end{pmatrix}+s\begin{pmatrix}2\\ 1\\ 1\\ -1\end{pmatrix}+t\begin{pmatrix}3\\ -2\\ 0\\ -1\end{pmatrix}\\ \text{These are the column vectors of matrix }A} \)