Solve {l}{a_{1}*b_{2}=a_{2}*b_{1}}{a=sqrt{2}}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { a_{1} \cdot b_{2} = a_{2} \cdot b_{1} }\\ { a = \sqrt{2} }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for a_1, b_2, a_2, b_1, a, b

$$a_{1}=\frac{a_{2}b_{1}}{b_{2}}\text{, }b_{2}\neq 0\text{, }a_{2}\in \mathrm{R}\text{, }b_{1}\in \mathrm{R}\text{, }a=\sqrt{2}\approx 1.414213562\text{, }b=\sqrt{2}\approx 1.414213562$$

$$a_{1}\in \mathrm{R}\text{, }b_{2}=0\text{, }a_{2}=0\text{, }b_{1}\in \mathrm{R}\text{, }a=\sqrt{2}\approx 1.414213562\text{, }b=\sqrt{2}\approx 1.414213562$$

$$a_{1}\in \mathrm{R}\text{, }b_{2}=0\text{, }a_{2}\in \mathrm{R}\text{, }b_{1}=0\text{, }a=\sqrt{2}\approx 1.414213562\text{, }b=\sqrt{2}\approx 1.414213562$$