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📰 Question: Planetary exploration engineers use a matrix $ \mathbf{M} $ to transform satellite coordinates. If $ \mathbf{M} \begin{bmatrix} 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 3 \\ -2 \end{bmatrix} $ and $ \mathbf{M} \begin{bmatrix} 0 \\ 1 \end{bmatrix} = \begin{bmatrix} 1 \\ 4 \end{bmatrix} $, find $ \mathbf{M} $. 📰 Solution: The columns of $ \mathbf{M} $ are the images of the standard basis vectors. Thus, $ \mathbf{M} = \begin{bmatrix} 3 & 1 \\ -2 & 4 \end{bmatrix} $. Verification: 📰 \mathbf{M} \begin{bmatrix} 1 \\ 0 \end{bmatrix} = 3 \cdot \begin{bmatrix} 1 \\ 0 \end{bmatrix} + 1 \cdot \begin{bmatrix} 0 \\ 1 \end{bmatrix} = \begin{bmatrix} 3 \\ -2 \end{bmatrix}, \quad \mathbf{M} \begin{bmatrix} 0 \\ 1 \end{bmatrix} = 1 \cdot \begin{bmatrix} 1 \\ 0 \end{bmatrix} + 4 \cdot \begin{bmatrix} 0 \\ 1 \end{bmatrix} = \begin{bmatrix} 1 \\ 4 \end{bmatrix}. 📰 Henry The Lions 1948986 📰 Vlc Media Player For Macbook 7692866 📰 Kicker For Colts 178512 📰 Problem 2 Derivative Of Wealth Function 9233812 📰 This Pro Trick Lets You Add Eye Catching Emojis In Outlooksee How 5147165 📰 Noel Noas Hidden Activation The Untold Truth Behind Her Ghostly Encounter 9797818 📰 Volleyball Legens 1897538 📰 Apple Tv Deals 2524121 📰 Send Money Wu 1808502 📰 S And P 500 Forecast 8213660 📰 Estella Marie Thompson 8546792 📰 Bathroom Wall Art 5565757 📰 This 2022 Ford Explorer Will Change How You See Every Single Detail 8203734 📰 Alaska Credit Card Annual Fee 3696911 📰 Kips Bay Court Apartments Nyc 2372753