Algebra Archive: Questions from October 12, 2022
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Question in English: Verify that the subset of R3 formed by the solutions of the following homogeneous system of equations is a subspace.
Verifique que el subconjunto de \( \mathbb{R}^{3} \) formado por las soluciones del siguiente sistema homogéneo de ecuaciones es un subespacio. \[ \left\{\begin{array}{l} x+y+z=0 \\ 2 x+3 y+4 z=0 \en2 answers -
Let V and U be two vector spaces over the reals. We denote by V ∩ U the intersection of the two vector spaces, that is, the subset of the elements that are in both spaces. Show that V ∩ U is a vec
3. Sean \( \mathbb{V} \) y \( \mathbb{U} \) dos espacios vectoriales sobre los reales. Denotamos por \( \mathbb{V} \cap \mathbb{U} \) la intersección de los dos espacios vectoriales, esto es, el subc1 answer -
Define \( \mathbf{A}=\left[\begin{array}{cc}2 & 3 \\ 1 & -2 \\ 0 & 1\end{array}\right] \) \[ \mathbf{B}=\left[\begin{array}{ccc} 5 & 0 & -3 \\ -2 & -2 & -3 \end{array}\right] \] 1. Evaluate: (i) IBIAI2 answers -
Define \( A=\left[\begin{array}{cc}2 & 3 \\ 1 & -2 \\ 0 & 1\end{array}\right] \) \[ B=\left[\begin{array}{ccc} 5 & 0 & -3 \\ -2 & -2 & -3 \end{array}\right] \] 1. Evaluate: (i) IBIAI (ii) (BA) \( { }^2 answers