53 lines
1.8 KiB
Markdown
53 lines
1.8 KiB
Markdown
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---
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title: How to Multiply Matrices
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---
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## How to Multiply Matrices
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The first immportant rule is: the number of columns in matrix A must match number of rows in column B.
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The second rule to calculate the product of two matrices is: Line X Column.
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<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Matrix_multiplication_principle.svg/320px-Matrix_multiplication_principle.svg.png" width="300" height="150">
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The resulting matrix dimension will be rows of first matrix X columns of second matrix.
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Let A and B be two matrices of dimension 2, that is, 2 X 2. Their product will be:
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<img src="http://www.i-programmer.info/images/stories/News/2011/DEC/A/matrix1.jpg" width="400" height="150">
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The rows of the the resuting matrix is the sum of product of first matrix row elements by second matrix column elements.
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#### Example
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Let A be a 2 X 3 matrix and B be a 3 X 2 matrix. The product AB will be:
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* **Step 1**
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<img src="http://www.mathportal.org/linear-algebra/matrices/matrix-operations_files/12.gif">
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* **Step 2**
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<img src="http://www.mathportal.org/linear-algebra/matrices/matrix-operations_files/13.gif">
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* **Step 3**
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<img src="http://www.mathportal.org/linear-algebra/matrices/matrix-operations_files/14.gif">
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* **Step 4**
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<img src="http://www.mathportal.org/linear-algebra/matrices/matrix-operations_files/15.gif">
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#### Attention!
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Differently from real numbers algebra, the product AB is not always equal to BA. Calculate it using the example above and find out.
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#### More Information:
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