Question

Evaluate the following:

{{1,2,3},{4,5,6},{7,8,9}} * {{7,4},{6,4},{5,3}}

Answer 1

Answer on Question #51653 - Math, Matrix - Tensor Analysis

Question. Evaluate the following:

$$\left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \right) \cdot \left( \begin{array}{cc} 7 & 4 \\ 6 & 4 \\ 5 & 3 \end{array} \right)$$

Solution.

$$\begin{array}{l} \left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \right) \cdot \left( \begin{array}{cc} 7 & 4 \\ 6 & 4 \\ 5 & 3 \end{array} \right) = \left( \begin{array}{cc} 1 \cdot 7 + 2 \cdot 6 + 3 \cdot 5 & 1 \cdot 4 + 2 \cdot 4 + 3 \cdot 3 \\ 4 \cdot 7 + 5 \cdot 6 + 6 \cdot 5 & 4 \cdot 4 + 5 \cdot 4 + 6 \cdot 3 \\ 7 \cdot 7 + 8 \cdot 6 + 9 \cdot 5 & 7 \cdot 4 + 8 \cdot 4 + 9 \cdot 3 \end{array} \right) \\ = \left( \begin{array}{cc} 7 + 12 + 15 & 4 + 8 + 9 \\ 28 + 30 + 30 & 16 + 20 + 18 \\ 49 + 48 + 45 & 28 + 32 + 27 \end{array} \right) \\ = \left( \begin{array}{cc} 34 & 21 \\ 88 & 54 \\ 142 & 87 \end{array} \right) \end{array}$$

Answer.

$$\left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \right) \cdot \left( \begin{array}{cc} 7 & 4 \\ 6 & 4 \\ 5 & 3 \end{array} \right) = \left( \begin{array}{cc} 34 & 21 \\ 88 & 54 \\ 142 & 87 \end{array} \right)$$

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