Algebra Archive: Questions from May 05, 2023
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Consider the vectors The vector a⃗ is expressed as the sum where c⃗ is parallel to b⃗ and d⃗ is perpendicular to b⃗. If d⃗ =(x,y,z), we can ensure that z is equal to:
\( \vec{a}=(1,-1,-29), \quad \) y \( \quad \vec{b}=(2,1,-1) \) \( \vec{a}=\vec{c}+\vec{d} \) Considere los vectores \[ \vec{a}=(1,-1,-29), \quad \text { y } \quad \vec{b}=(2,1,-1) \] El vector \( \v0 answers -
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1. Sean el espacio vectorial \( \mathbb{C}^{2}=\left\{\left(z_{1}, z_{2}\right) \mid z_{1}, z_{2} \in \mathbb{C}\right\} \) sobre el campo \( K \) y \( W=\{(z, z-\bar{z}) \mid z \in \mathbb{C}\} \) un2 answers -
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Is \( T: R^{3} \rightarrow R^{3}, T(x, y, z)=(x, x+y, y+z) \) a linear transformation? Justify your answer!2 answers -
4) find the standard matrix for: \( \quad T=T_{2} \circ T_{1} \) \[ \begin{array}{l} T_{1}: R^{2} \rightarrow R^{3} \quad T_{1}(x, y)=(x, y, x+y) \\ T_{2}: R^{3} \rightarrow R^{2} \quad T_{2}(x, y, z)2 answers -
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