Define the matrices A=\left[\begin{array}{ccc} 2&3\\ {1}&{-5}\end{array}\right] and B=\left[\begin{array}{ccc} 4&3&6\\ {1}&3.9&3\end{array}\right]. What is the entry in the first row and second column of AB?
Question
Define the matrices
A=\left[\begin{array}{ccc} 2&3\ {1}&{-5}\end{array}\right] and B=\left[\begin{array}{ccc} 4&3&6\ {1}&3.9&3\end{array}\right].
What is the entry in the first row and second column of AB?
Solution
To find the entry in the first row and second column of the product of two matrices, we multiply each element in the first row of the first matrix by the corresponding element in the second column of the second matrix, and then sum these products.
For matrices A and B given, the first row of A is [2, 3] and the second column of B is [3, 3.9].
So, the entry in the first row and second column of AB is (23) + (33.9) = 6 + 11.7 = 17.7.
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