Algebra Archive: Questions from November 28, 2022
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1. In each part, determine whether \( T \) is LT. \( \begin{array}{ll}\text { (a) } T(x, y, z)=(0,0) & \text { (b) } T(x, y, z, w)=(1,-1)\end{array} \) (c) \( T(x, y, z)=(x-y+z \), 0) (d) \( T(x, y, z1 answer -
Solve for \( x \) and \( y \). \[ \left[\begin{array}{cc} -6 & 3 \\ 4 & 6 \end{array}\right]\left[\begin{array}{cc} -5 & x \\ -3 & y \end{array}\right]=\left[\begin{array}{cc} 21 & -15 \\ -38 & 2 \end2 answers -
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(6) \( \frac{d y}{d x}+2 y=e^{\prime} \quad \) Linear in \( y \) (7) \( \left.(x-1)^{3} \frac{d y}{d x}+\frac{4(x-1)}{\frac{x^{3}}{3}-x+c}\right) y=x+1 \) "Linear in \( y^{\circ} \) (2) \( \left(y^{2}2 answers -
Help plz Consider linear transformation 1 2 3 1 1 2 3 L x x x x x x x ( , , ) ( , ) of 3 a two . a. (8%) Prove that L is a linear transformation. b. (5%) Find a basis for the kernel of L.
1. Considerar la transformación lineal \( L\left(x_{1}, x_{2}, x_{3}\right)=\left(x_{1}, x_{1}+x_{2}-x_{3}\right) \) de \( \mathbb{R}^{3} \) a \( \mathbb{R}^{2} \). a. (8\%) Demostrar que \( L \) es0 answers -
1. Considerar la transformación lineal \( L\left(x_{1}, x_{2}, x_{3}\right)=\left(x_{1}, x_{1}+x_{2}-x_{3}\right) \) de \( \mathbb{R}^{3} \) a \( \mathbb{R}^{2} \). a. \( (8 \%) \) Demostrar que \( L2 answers -
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