![1)A*B= \left[\begin{array}{ccc}1&-4&1\\0&-2&2\\-1&1&3\end{array}\right] * \left[\begin{array}{ccc}1\\2\\3\end{array}\right] = \left[\begin{array}{ccc}-4\\2\\10\end{array}\right]](https://tex.z-dn.net/?f=1%29A%2AB%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-4%261%5C%5C0%26-2%262%5C%5C-1%261%263%5Cend%7Barray%7D%5Cright%5D+%2A++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C2%5C%5C3%5Cend%7Barray%7D%5Cright%5D+%3D+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%5C%5C2%5C%5C10%5Cend%7Barray%7D%5Cright%5D+ "1)A*B= \left[\begin{array}{ccc}1&-4&1\\0&-2&2\\-1&1&3\end{array}\right] * \left[\begin{array}{ccc}1\\2\\3\end{array}\right] = \left[\begin{array}{ccc}-4\\2\\10\end{array}\right]")
//
c11 = a11
· b11 + a12
· b21 + a13
· b31 = 1 · 1 + (-4) · 2 + 1 · 3 = 1 - 8 + 3 = -4
c21 = a21
· b11 + a22
· b21 + a23
· b31 = 0 · 1 + (-2) · 2 + 2 · 3 = 0 - 4 + 6 = 2
c31 = a31
· b11 + a32
· b21 + a33
· b31
= (-1) · 1 + 1 · 2 + 3 · 3 = (-1) + 2 + 9 = 10
//
![2) 2*C = 2* \left[\begin{array}{ccc}0\\2\\3\end{array}\right] = \left[\begin{array}{ccc}0\\4\\6\end{array}\right]](https://tex.z-dn.net/?f=2%29+2%2AC+%3D++2%2A+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%5C%5C2%5C%5C3%5Cend%7Barray%7D%5Cright%5D++%3D+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%5C%5C4%5C%5C6%5Cend%7Barray%7D%5Cright%5D+ "2) 2*C = 2* \left[\begin{array}{ccc}0\\2\\3\end{array}\right] = \left[\begin{array}{ccc}0\\4\\6\end{array}\right]")
![3) \left[\begin{array}{ccc}-4\\2\\10\end{array}\right] - \left[\begin{array}{ccc}0\\4\\6\end{array}\right] = \left[\begin{array}{ccc}-4-0\\2-4\\10-6\end{array}\right] = \left[\begin{array}{ccc}-4\\-2\\4\end{array}\right]](https://tex.z-dn.net/?f=3%29++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%5C%5C2%5C%5C10%5Cend%7Barray%7D%5Cright%5D++-+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%5C%5C4%5C%5C6%5Cend%7Barray%7D%5Cright%5D+++%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4-0%5C%5C2-4%5C%5C10-6%5Cend%7Barray%7D%5Cright%5D+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%5C%5C-2%5C%5C4%5Cend%7Barray%7D%5Cright%5D+++ "3) \left[\begin{array}{ccc}-4\\2\\10\end{array}\right] - \left[\begin{array}{ccc}0\\4\\6\end{array}\right] = \left[\begin{array}{ccc}-4-0\\2-4\\10-6\end{array}\right] = \left[\begin{array}{ccc}-4\\-2\\4\end{array}\right]")