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Home » Set \( 4\pi r^2 = 144\pi \). - SUpost

Set \( 4\pi r^2 = 144\pi \). - SUpost

📅 July 5, 2026 👤 scraface

Jul 05, 2026

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📌 oxed{30^\circ, 90^\circ, 150^\circ, 270^\circ}

📌 An electrical engineer is optimizing a power grid model and encounters a transformation matrix problem. Find the \(2 imes 2\) matrix \(\mathbf{M}\) such that for any vector \(\mathbf{v} = egin{bmatrix} x \ y \end{bmatrix}\), the transformation satisfies \(\mathbf{M}\mathbf{v} = egin{bmatrix} x + 2y \ 3x - y \end{bmatrix}\).

📌 We are given a linear transformation defined by:

📌 \mathbf{M} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} x + 2y \ 3x - y \end{bmatrix}

📌 This implies that \(\mathbf{M}\) transforms \((x, y)\) into \((x + 2y, 3x - y)\). We express this transformation using matrix multiplication:

📌 \mathbf{M} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} a & b \ c & d \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} ax + by \ cx + dy \end{bmatrix}

📌 Equating components:

📌 ax + by = x + 2y \quad \Rightarrow \quad a = 1, \; b = 2

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