Question #2028054: linear algebra

Question: Consider the complex vector space ${{\mathbb{C}}^{2}}=\left\{ \left( {{z}_{1}},{{z}_{2}} \right):\,\,{{z}_{1}},{{z}_{2}}\in \mathbb{C} \right\}$. For each element $\left( {{z}_{1}},{{z}_{2}} \right)\in {{\mathbb{C}}^{2}}$ find complex numbers $\alpha$ and $$\beta$$ for which

$\left( {{z}_{1}},{{z}_{2}} \right)=\alpha \left( 1+i,1-i \right)+\beta \left( 2+i,2-i \right)$

Do $$\left( 1+i,1-i \right)$$ and $$\left( 2+i,2-i \right)$$ form a linearly independent pair in $${{\mathbb{C}}^{2}}$$ ? Do $$\left( 1+i,1-i \right)$$ and $$\left( 2+i,2-i \right)$$ span $${{\mathbb{C}}^{2}}$$ ?

Solution: The solution consists of 222 words (2 pages)
Deliverables: Word Document

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