Given: \( a^{2}-5 a b+4 b^{2}=0 \) (1) Solve for \( a \) in terms of \( b \).

Solve the equation \( a^{2}-5ab+4b^{2}=0 \). Solve the equation by following steps: - step0: Solve for \(a\): \(a^{2}-5ab+4b^{2}=0\) - step1: Rewrite the expression: \(a^{2}-5ba+4b^{2}=0\) - step2: Factor the expression: \(\left(a-b\right)\left(a-4b\right)=0\) - step3: Separate into possible cases: \(\begin{align}&a-b=0\\&a-4b=0\end{align}\) - step4: Solve the equation: \(\begin{align}&a=b\\&a=4b\end{align}\) The solutions for \( a \) in terms of \( b \) are \( a = b \) and \( a = 4b \).