Algebra Archive: Questions from May 16, 2023
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8. Solve in \( [0, \pi] \) the system of equations \[ \begin{aligned} 2 \sin ^{2} x \sin ^{2} y+\cos x \cos y & =\frac{7}{8} \\ 2 \cos ^{2} x \cos ^{2} y-3 \sin x \sin y & =-\frac{17}{8} \end{aligned}0 answers -
I need help on this practical about linear algebra with the step
Si \( \lambda \) es un autovalor de una matriz \( A \), muestre que \( \lambda^{5} \) es un autovalor de \( A^{5} \).2 answers -
I need help on this practical about linear algebra with the step
\( T: \mathbf{M}_{2 \times 2} \rightarrow \mathbf{M}_{2 \times \mathbf{2}} \) representado por \( T(A)=A^{t} \) (transpuesta de A). Hallar la matriz asociada a \( T \) con respecto a las bases estánd2 answers -
Let \( x, y, z \) be (non-zero) vectors and suppose \( w=-16 x-16 y-2 z \). If \( z=-4 x-4 y \), then \( w=\quad x+\quad y \) Using the calculation above, mark the statements below that must be true.2 answers -
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determinar el valor numérico de escalares
Determina el valor numérico de los escalares \( \mathbf{a}_{1}, \mathbf{a}_{2} \) y a a \( _{3} \) para que el vector \( \mathbf{v}=(-1,-21,-19) \) se exprese como una combinación lineal de los vect2 answers -
Encontrar la matriz de transición
La matriz de transición en \( \Re^{2} \) de la base \( \left\{\left(\begin{array}{l}1 \\ 0\end{array}\right),\left(\begin{array}{l}0 \\ 1\end{array}\right)\right\} \) a la base \( \left\{\left(\begin2 answers -
Escribe una base ortonormal para un espacio vectorial
Escribe una base ortonormal para el espacio vectorial \( \left\{\left(\begin{array}{c}V_{1} \\ 6 \\ -3\end{array}\right),\left(\begin{array}{c}V_{2} \\ -5 \\ 2\end{array}\right)\right\} \)2 answers -
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1. Resuelva \( \mathbf{y} \) dibuje cada uno de los vectores indicados. (Los vectores u y \( \mathbf{v} \) se muestran en la figura). a) \( 2 u \) b) \( -v \) c) \( u+v \) d) \( u=v \) e) \( v-2 u \)2 answers -
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Prove if \[ \begin{array}{l} a \equiv a^{\prime}(\operatorname{modm}) \\ b \equiv b^{\prime}(\bmod m) \\ c \equiv c^{\prime}(\operatorname{modm}) \end{array} \] then \( \quad a b c \equiv a^{\prime} b2 answers -
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