Question

7．若線性方程組的增廣矩陣為$（\begin{array}{l}{2}&{3}&{{c}_{1}}\\{3}&{2}&{{c}_{2}}\end{array}）$，解為$\left\{\begin{array}{l}x=2\\ y=1\end{array}\right.$，則c₁-c₂=-1．

Answer 1

分析 由增廣矩陣的定義先分別求出c₁，c₂，由此能求出c₁-c₂的值．

解答 解：∵線性方程組的增廣矩陣為$（\begin{array}{l}{2}&{3}&{{c}_{1}}\\{3}&{2}&{{c}_{2}}\end{array}）$，解為$\left\{\begin{array}{l}x=2\\ y=1\end{array}\right.$，
∴$\left\{\begin{array}{l}{{c}_{1}=2×2+3=7}\\{{c}_{2}=3×2+2=8}\end{array}\right.$，
∴c₁-c₂=7-8=-1．
故答案為：-1．

點(diǎn)評(píng) 本題考查代數(shù)式的值的求法，是基礎(chǔ)題，解題時(shí)要認(rèn)真審題，注意增廣矩陣的定義及性質(zhì)的合理運(yùn)用．