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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}. 📰 Cast Of Two Broke Chicks 6197209 📰 Now Compute The Sector Area Rac120360 Imes 100Pi Rac13 Imes 100Pi Rac100Pi3 Pprox 10472 Ext Cm2 3606550 📰 Discover The Secret Origins Of The Bulgarian Flag You Never Knew 1890653 📰 Helix Jump Unblocked The Shocking Reason You Need This Game Changing Jump Move 5833602 📰 Finally Hear The Differencedownload Sound Connect App Today Transform Listening 2238449 📰 Master Instagram Success With Instatikstop Guessing Start Succeeding 4770898 📰 You Wont Believe What Your Client Portal Can Do To Transform Your Business 264538 📰 A Historian Of Science Is Analyzing The Publication Dates Of Two Seminal Papers The First Paper Was Published In 1675 And The Second In 1715 If The Ratio Of Years Between Their Publications Is Expressed In Base 2 What Is The Binary Representation Of This Ratio 9447338 📰 Diane Dinklage 2297120 📰 Video Games Free Download 2850201 📰 Spacex Market Cap Explodeswhat This Game Changer Means For Investors 2281758 📰 Wry Smile 5116412 📰 Afv Comedy 6644931 📰 From Solitude To Terror The Hidden Horror Of The Dark Alone You Wont Discover Everywhere 9405409 📰 Discover The Secret To Oracle Advanced Compressionmaximize Storage Efficiency Today 5211435