Multiplying Matrices
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To multiply matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The resulting matrix will have the number of rows of the first and the number of columns of the second. For example, a matrix with dimensions axb can be multiplied with a bxc matrix to produce an axc resulting matrix.
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![In order to be able to multiply matrices together, they must be of the format [axb].[bxc]](https://image.slidesharecdn.com/multiplyingmatrices-110726005141-phpapp02/85/Multiplying-Matrices-1-320.jpg)
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See also:
http://www.slideshare.net/JamesSmith245/rotations-of-vectors-via-geometric-algebra-explanation-and-usage-in-solving-classic-geometric-construction-problems-version-of-11-february-2016 ;
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http://www.slideshare.net/JamesSmith245/solution-of-the-special-case-clp-of-the-problem-of-apollonius-via-vector-rotations-using-geometric-algebra ;
http://www.slideshare.net/JamesSmith245/solution-of-the-ccp-case-of-the-problem-of-apollonius-via-geometric-clifford-algebra ;
http://www.slideshare.net/JamesSmith245/a-very-brief-introduction-to-reflections-in-2d-geometric-algebra-and-their-use-in-solving-construction-problems ;
http://www.slideshare.net/JamesSmith245/solution-of-the-llp-limiting-case-of-the-problem-of-apollonius-via-geometric-algebra-using-reflections-and-rotations ;
http://www.slideshare.net/JamesSmith245/simplied-solutions-of-the-clp-and-ccp-limiting-cases-of-the-problem-of-apollonius-via-vector-rotations-using-geometric-algebra ;
http://www.slideshare.net/JamesSmith245/additional-solutions-of-the-limiting-case-clp-of-the-problem-of-apollonius-via-vector-rotations-using-geometric-algebra ;
http://www.slideshare.net/JamesSmith245/an-additional-brief-solution-of-the-cpp-limiting-case-of-the-problem-of-apollonius-via-geometric-algebra-ga .
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- 1. In order to be able to multiply matrices together, they must be of the format [axb].[bxc]
- 2. In order to be able to multiply matrices together, they must be of the format [axb].[bxc] The resulting matrix is axc
- 3. In order to be able to multiply matrices together, they must be of the format [axb].[bxc] The resulting matrix is axc In other words, the number of columns in the first matrix must be equal to the number of rows in the second
- 4. In order to be able to multiply matrices together, they must be of the format [axb].[bxc] The resulting matrix is axc In other words, the number of columns in the first matrix must be equal to the number of rows in the second Thus, the answer is b and c
- 5. So the problem we need to solve is x
- 6. To multiply matrices, we go row by column x
- 7. To multiply matrices, we go row by column x =
- 8. Take the sum of the products of corresponding elements x = Here we have (4*10)+(1*1)+(2*5)+(6*2)= 40+1+10+12=63 So 63 goes in this circle
- 9. Take the sum of the products of corresponding elements x = Here we have (4*10)+(1*1)+(2*5)+(6*2)= 40+1+10+12=63 So 63 goes in this circle
- 10. Continuing this process, we get x = As desired, we get a 3x2 matrix!