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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}. 📰 Waitheres A Refined 5 Clickbait Seo Optimized List For Hope Chest 9671837 📰 Current Weather Carmel Indiana 2572078 📰 The Smurfs The Movie 2834424 📰 Pro Tip To Game Like A Pro On Gta 5 Ps4Watch These Essential Hacks Go Viral 8368003 📰 This Omnichannel Retailing Strategy Boosted Customer Loyalty By 90Dont Miss It 692900 📰 Why This Mexican Train Dominoes Game Is Taking The Internet By Storm 8952173 📰 Foci Definition 4347501 📰 Americas Favorite Wall Installs Its First Throne At The Big Game 5605697 📰 Gallbladder Disease Symptoms 6894364 📰 How To Change Default Font In Word 9953887 📰 Alternative Maybe First Term Is 1 But Says 5 6400715 📰 Can Steffes Be The Game Changer Normally Hidden Genius Revealed 1576999 📰 Alfred Lord Tennyson Poems 2938110 📰 Sarcastic New Year Memes 4465540 📰 How Tall Is Kai Trump 2627983