Question

17．设A=$（\begin{array}{l}{3}&{0}&{4}\\{-1}&{5}&{2}\end{array}）$，B=$（\begin{array}{l}{1}&{0}\\{0}&{-1}\\{1}&{1}\end{array}）$，则AB=$[\begin{array}{l}{7}&{4}\\{1}&{-3}\end{array}]$．

Answer 1

分析 利用矩阵与矩阵相乘的法则直接求解．

解答 解：∵A=$（\begin{array}{l}{3}&{0}&{4}\\{-1}&{5}&{2}\end{array}）$，B=$（\begin{array}{l}{1}&{0}\\{0}&{-1}\\{1}&{1}\end{array}）$，
∴AB=$（\begin{array}{l}{3}&{0}&{4}\\{-1}&{5}&{2}\end{array}）$$（\begin{array}{l}{1}&{0}\\{0}&{-1}\\{1}&{1}\end{array}）$=$[\begin{array}{l}{7}&{4}\\{1}&{-3}\end{array}]$．
故答案为：$[\begin{array}{l}{7}&{4}\\{1}&{-3}\end{array}]$．

点评 本题考查矩阵的乘积的求法，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．