Algebra Archive: Questions from March 15, 2023
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Use Cramer's rule to solve for \( x^{\prime} \) and \( y^{\prime} \) in terms of \( x \) and \( y \). \[ \begin{array}{l} x=x^{\prime} \cos \theta-y^{\prime} \sin \theta \\ y=x^{\prime} \sin \theta+y^2 answers -
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Ejercicio 1: Verifica si la siguiente operación es una Transformación Lineal \[ T\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{c} \frac{1}{2} x \\ y \end{array}\right] \] Ejer2 answers -
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Let \( T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3} \) be the projection \( T(u)=\operatorname{proj}_{\mathrm{v}}(\mathrm{u}) \) where \( \mathrm{v}=(1,-1,2) \). Find \( T(x, y, z) \). [Recall that \(2 answers