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Home Question Bank Math Algebra Archive 2024 November 28

Algebra Questions from Nov 28,2024

Browse the Algebra Q&A Archive for Nov 28,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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(4) Resolver el sistema \( \begin{array}{l}4 x+6 y=2 \\ 6 x+5 y=1\end{array} \) \( \begin{array}{ll}6 x+6 y=2 & 6 x+5 y=1 \\ 4 x=2-6 y & x=1-5 y \\ x+2-6 y & x=1-5 y\end{array} \) Express in radical form \( (2 x)^{\frac{1}{2}} \) (iv) \( -x^{2}+3 x+20=0 \) \( 2 \begin{array}{l}\text { To simplify }\left(5 x^{\frac{2}{3}} y^{\frac{2}{5}}\right)^{\frac{1}{7}} \text {, what will you do with the exponents? } \\ \begin{array}{ccc}\text { A. add } & \text { B. divide } & \text { C. multiply }\end{array} \quad \text { D. subtract }\end{array} \) 3. (Valor 1.0) Determinar cúal de los siguientes subconjuntos es un subespa- cio del espacio vectorial indicado. \( S_{1}=\left\{\left(x_{1}, x_{2}\right) \in \mathrm{R}^{2} \mid \alpha=\left(1, x_{2}\right), x_{2} \in \mathrm{R}\right\} \) \( S_{2}=\left\{\left(x_{1}, x_{2}, x_{3}\right) \in \mathrm{R}^{3} \mid x_{1}^{2}+x_{2}^{2}+x_{3}^{3}=k ; k \in \mathrm{Z}_{0}^{+}\right\} \) \( S_{3}=\left\{\left(x_{1}, x_{2}, x_{3}, x_{4}\right) \in \mathrm{R}^{4} \mid \alpha=a(1,-1,0,2)+b(0,2,1,-1), a, b \in \mathrm{R}\right\} \) 4. (Valor 1.0) Pruebe que gen \( (1, x)= \) gen \( (2+3 x, x) \). 5. (Valor 1.0) Encuentre una base para el subespacio de \( \mathbf{R}^{4} \) generado por los vectores. \( \left[\begin{array}{llll}1 & -1 & 2 & 1\end{array}\right]^{T} ;\left[\begin{array}{llll}-1 & 2 & -3 & 1\end{array}\right]^{T} ;\left[\begin{array}{lllll}-1 & 3 & -3 & 1\end{array}\right]^{T} ;\left[\begin{array}{llll}2 & 1 & 2 & 6\end{array}\right]^{T} \) 30) \( -7 x=0 \) 31) \( 2=4-2 x \) 32) \( 2-12 x=0 \) 33) \( 2 x-3=1 \) 34) \( 14=2 x+6 \) 35) \( 3 x-4=8 \) 36) \( 4 x+7=35 \) 37) \( 5-3 x=-4 \) 3. Given the functions \( f(x)=2 x-1 \) and \( g(x)=\frac{1}{3} x^{2} \), show that \( (f \circ g)^{-1}=g^{-1} \circ f^{-1} \). Let \( A=\left[\begin{array}{ll}1 & -1 \\ 7 & -2\end{array}\right] \) Find \( -4 A \) Find \( x \) \( \frac{x}{\frac{30^{\circ}}{9}} \) 1. \( \left\{\begin{array}{l}2 x+3 y=20\} \\ x-2 y-3\end{array}\right\} \)
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