Algebra Archive: Questions from June 02, 2023
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Consider the π plane with equation x+3y−30z=0. if the vectors form an orthogonal basis of π, then the value of α+β is:
Considere el plano \( \pi \) con ecuación \( x+3 y-30 z=0 \) Si los vectores \[ \vec{v}_{1}=\left(\begin{array}{c} -3 \\ 1 \\ 0 \end{array}\right), \quad \vec{v}_{2}=\left(\begin{array}{c} \alpha \\2 answers -
Let S be a vector subspace of R4 spanned by the 3 vectors v⃗ Let v⃗ be the vector v⃗ Then, if the orthogonal projection of v⃗ onto S is the vector ProjSv⃗ = the value of w is: Note: the set
Sea \( S \) subespacio vectorial de \( \mathbb{R}^{4} \) generado por los 3 vectores \[ \vec{v}_{1}=\left(\begin{array}{l} 1 \\ 2 \\ 0 \\ 2 \end{array}\right), \vec{v}_{2}=\left(\begin{array}{c} -1 \\2 answers -
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3. Una compañia minera extrae mineral de dos minas, el cual contiene para la mina I el \( 1 \% \) de niquel y \( 2 \% \) de cobre, para la mina II el \( 2 \% \) de niquel y \( 5 \% \) de cobre. ¿Qu2 answers -
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4. Para la matriz dada obtener lo que se le indica. (20 puntos) \[ \left(\begin{array}{ccc} -2 & 2 & 3 \\ -2 & 1 & -1 \\ 4 & 0 & -4 \end{array}\right) \quad A= \] a) \( M_{31} \) b) \( \mathrm{A}_{32}2 answers