Question

5．已知矩陣A=$（{\begin{array}{l}1&2\\ y&4\end{array}}）$，B=$（{\begin{array}{l}x&6\\ 7&8\end{array}}）$，AB=$（{\begin{array}{l}{19}&{22}\\{43}&{50}\end{array}}）$，則x+y=8．

Answer 1

分析 利用矩陣乘法法則求解．

解答 解：∵矩陣A=$（{\begin{array}{l}1&2\\ y&4\end{array}}）$，B=$（{\begin{array}{l}x&6\\ 7&8\end{array}}）$，AB=$（{\begin{array}{l}{19}&{22}\\{43}&{50}\end{array}}）$，
∴AB=$[\begin{array}{l}{1}&{2}\\{y}&{4}\end{array}]$$[\begin{array}{l}{x}&{6}\\{7}&{8}\end{array}]$=$[\begin{array}{l}{x+14}&{22}\\{xy+28}&{6y+32}\end{array}]$=$[\begin{array}{l}{19}&{22}\\{43}&{50}\end{array}]$，
∴$\left\{\begin{array}{l}{x+14=19}\\{xy+28=43}\\{6y+32=50}\end{array}\right.$，解得x=5，y=3，
∴x+y=8．
故答案為：8．

點評 本題考查代數式的值的求法，是基礎題，解題時要認真審題，注意矩陣乘法法則的合理運用．