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Exercise 4.3.2

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Since we have the condition $\det (\begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{matrix}) = a_{11} a_{22} - a_{12} a_{21} \neq 0$ , we can use Cramer’s rule and get the answer.

{\begin{matrix} x_{1} & = \frac{\det (\begin{matrix} b_{1} & a_{12} \\ b_{2} & a_{22} \end{matrix})}{\det (\begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{matrix})} = \frac{b_{1} a_{22} - a_{12} b_{2}}{a_{11} a_{22} - a_{12} a_{21}}, \\ x_{2} & = \frac{\det (\begin{matrix} a_{11} & b_{1} \\ a_{21} & b_{2} \end{matrix})}{\det (\begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{matrix})} = \frac{a_{11} b_{1} - b_{2} a_{21}}{a_{11} a_{22} - a_{12} a_{21}} . \end{matrix}

jephianlin

2011-06-27 00:00

Exercise 4.3.2

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