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Al aplicar el principio de dualidad a la expresión \( X+X^{\prime}=1 \) (donde \( X \) es el complemento de \( X \) ), el resultado es: a. \( \quad X \cdot X^{\prime}=1 \) b. \( \quad X+X=X \) c. \( \quad X \cdot X^{\prime}=0 \) d. \( \quad X+X^{\prime}=0 \)
Colombia Dec 18, 2024
Multiply \( (7-4 i) \cdot(-7+4 i) \) to prove that they are not conjugates. Explain how your answer proves they are NOT conjugates. SHOW MULTIPLICATION STEPS
United States Dec 18, 2024
Université Paris 8 Méthode de Gauss pour les formes quadratiques Exercice 1. Soit \( E \) un espace vectoriel de dimension 3 sur \( \mathbb{R} \). Montrer que l'applicat \( \varphi: E \times E \rightarrow \mathbb{R} \) telle que \( \quad \varphi(u, v)=2 u_{1} v_{1}+u_{2} v_{2}+2 u_{3} v_{3}-2\left(u_{1} v_{2}+u_{2} v_{1}\right)+2\left(u_{1} v_{3}+u_{3} v_{1}\right)-\left(u_{2} v_{3}+u_{3} v_{2}\right) \) n'est pas un produit scalaire.
France Dec 18, 2024
Exercice 2. Soient \( E=\mathbb{R}^{3}, h \in \mathbb{R} \) un paramètre et \( \varphi_{h}: E \times E \rightarrow \mathbb{R} \) une application bilinéaire et symétrique telle que \[ \varphi_{h}(u, v)=2 u_{1} v_{1}+2\left(u_{1} v_{2}+u_{2} v_{1}\right)+3 u_{2} v_{2}+(h-1) u_{3} v_{3}, \] où \( u=\left(u_{1}, u_{2}, u_{3}\right)^{t}, v=\left(v_{1}, v_{2}, v_{3}\right)^{t} \) sont deux vecteurs de \( \mathbb{R}^{3} \) en base canonique. (a) Montrer que la matrice \( \Phi_{h} \) associée à \( \varphi_{h} \) en base canonique est la suivante \[ \Phi_{h}=\left(\begin{array}{ccc}2 & 2 & 0 \\ 2 & 3 & 0 \\ 0 & 0 & h-1\end{array}\right), \] ce qui signifie que Prouver aussi, par la méthode de Gauss, que \( \varphi_{h} \) est un produit scalaire si et seulement si \( h>1 \).
France Dec 18, 2024
Find the rank of matrix \( A=\left[\begin{array}{ccc}3 & -1 & 2 \\ -6 & 2 & -4 \\ -3 & 1 & -2\end{array}\right. \)
India Dec 18, 2024
EJERCICIO 2: Estudia el rango de la matriz. \( E=\left(\begin{array}{lll}1 & 2 & a \\ 1 & 1 & a \\ a & 0 & 1\end{array}\right) \) según los valores del parámetro "a" ¿existe algún valor de a para que el rango (E)=1? ¿Puede decir si es invertible la matriz E?. Recuerde que para analizar el rango de una matriz, escalonábamos por medio de Gauss (25\%)
Argentina Dec 18, 2024
Exercice 1. Soit \[ A_{k}=\left[\begin{array}{cccc}1 & 0 & 1 & 0 \\ -k & 1 & 1 & -k \\ k & 0 & 0 & k \\ -1+k & 0 & -1 & k\end{array}\right] \in \text { Mat }{ }_{4}(\mathbb{R}) . \] (a) Montrer que \( \chi_{A_{4}}(x)=x(x-k)(x-1)^{2} \). (b) Montrer que pour \( k \neq 0 \) and \( k \neq 1 \) la matrice \( A_{k} \) est diagonalisable. (c) Montrer que pour \( k=1 \) la matrice \( A_{1} \) n'est pas diagonalisable. (d) Montrer que pour \( k=0 \) la matrice \( A_{0} \) est diagonalisable et trouver une base de \( \mathbb{R}^{4} \) formée par des vecteur propres pour \( A_{0} \).
France Dec 18, 2024
La qualité de la rédaction sera prise en compte. Exercice 1. Soit \[ A_{k}=\left[\begin{array}{cccc}1 & 0 & 1 & 0 \\ -k & 1 & 1 & -k \\ k & 0 & 0 & k \\ -1+k & 0 & -1 & k\end{array}\right] \in \text { Mat }_{4}(\mathbb{R}) \] (a) Montrer que \( \chi_{A_{4}}(x)=x(x-k)(x-1)^{2} \). (b) Montrer que pour \( k \neq 0 \) and \( k \neq 1 \) la matrice \( A_{k} \) est diagonalisable. (c) Montrer que pour \( k=1 \) la matrice \( A_{1} \) n'est pas diagonalisable. (d) Montrer que pour \( k=0 \) la matrice \( A_{0} \) est diagonalisable et trouver une base de \( \mathbb{R}^{4} \) formée par des vecteur propres pour \( A_{0} \).
France Dec 18, 2024
77. In a secondary treatment activated sludge plant, the primary c \( 40 \% \) of the influent BOD and the activated sludge process rem primary effluent BOD. If the plant's influent BOD is \( 245 \mathrm{mg} / \mathrm{L} \), concentration of BOD in the effluent?
Canada Dec 18, 2024
¿Qué son los números primos y por qué son importantes?
Spain Dec 18, 2024
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