Question

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

Answer 1

分析 利用矩阵乘法法则求解．

解答 解：∵矩阵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．
故答案为：8．

点评 本题考查代数式的值的求法，是基础题，解题时要认真审题，注意矩阵乘法法则的合理运用．