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Other Questions from Dec 16,2024

Browse the Other Q&A Archive for Dec 16,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Which of the following allows the telecommunications industry to transmit the greatest volume of data the fastest speed? Se pensar Selecciona la respuesta correcta, la siguiente proposició compuesta es una: \( \neg(\boldsymbol{p} \vee \boldsymbol{q}) \rightarrow(\boldsymbol{p} \rightarrow \boldsymbol{r}) \) Tautología. Contradiecion. Contingencia. Ninguna de las anteriores. For the linear transformation \( L: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3} \) given by \[ L((x, y))=(x+2 y,-x, 0) \] find the matrix \( A_{B C} \) for \( L \) with respect to the bases \[ B=\{(1,3),(-2,4)\}, C=\{(1,1,1),(2,2,0),(3,0,0)\} \] s) For the linear transformation \( L: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3} \) given by \[ L((x, y))=(x+2 y,-x, 0) \] find the matrix \( A_{B C} \) for \( L \) with respect to the bases \[ B=\{(1,3),(-2,4)\}, C=\{(1,1,1),(2,2,0),(3,0,0)\} \] (20 points) Let \( v=(-5,8,-5) \in \mathbf{R}^{3} \). Let \( B \) and \( C \) be bases of \( \mathbf{R}^{3} \) \[ B=\{(2,1,1),(2,-1,1),(1,2,1)\}, C=\{(3,1,-5),(1,1,-3),(-1,0,2)\} . \] Find the coordinates \( [v]_{B} \) of vector \( v \) with respect to \( B \). Find the transition matrix \( P \) from \( B \) to \( C \). Using \( [v]_{B} \) and \( P \) find \( [v]_{C} \). For the linear transformation \( L: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3} \) given by \[ L((x, y))=(x+2 y,-x, 0) \] find the matrix \( A_{B C} \) for \( L \) with respect to the bases \[ B=\{(1,3),(-2,4)\}, C=\{(1,1,1),(2,2,0),(3,0,0)\} \] Do vectors \( v_{1}=(-8,2,-3,2), v_{2}=(4,1,-5,-4), v_{3}=(-3,-1,4,3), v_{4}=(2,-1,0,-1) \) form a basis of \( R^{4} \) ? Answer this question by using 3.1 Simplified Span Method (Andrilli p.232) 3.2 Independence test method (Andrilli p.242) "There are two extremes of balance. . . which he who has given up the world ought to avoid. What are these two extremes? A life given to pleasures, devoted to pleasures and lusts: this is degrading, sensual, vulgar, ignoble, and profitless; and a life given to mortifications: this is painful, ignoble, and profitless." -The Buddha, Sermon at Benares 23. (2.2, 2.3; DOK 3) In the excerpt from the Buddha's sermon, Buddha taught about nirvana. Mahabharata. O the Middle Way. EXERCICE 08 Soí \( \left(u_{n}\right) \) une suite numérique définie par: \[ \left\{\begin{array}{c}u_{0}=\frac{1}{2} \\ (\forall n \subseteq \mathbb{N}) ; u_{n+1}=\frac{3 u_{n}+3}{u_{n}+6}\end{array}\right. \] 1) a-Montrer que \( \left(\forall n \in \mathbb{N}^{*}\right) ; 1<u_{n}<3 \). b- Montrer que la suite \( \left(u_{n}\right) \) est croissante 2) On considère la suite \( \left(v_{n}\right) \) définie par: \( (\forall n \in \mathbb{N}) ; v_{n}=\frac{u_{n}-3}{u_{n}+1} \) \( \begin{array}{l} U=\{\text { Vitamins }\} \\ A=\{\text { Vits } B, \text { Vit B12, Folate }\} \\ B=\{\text { Vit K, Vit } C, \text { Calcium }\} \\ \text { (a) Show these sets on a Venn diagram } \\ \text { (b) List the elements of } A \cap B \\ \text { (c) List the elements of } A^{\prime} \\ \text { (d) List the elements of } A^{\prime} \cup B\end{array} \)
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