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How To Multiply Matrices 3x3



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Question
How do I do this in Microsoft Excel?
I need to multiply two matrices. A 3x3 and a1x3. What Excel function/formula can I use to calculate the product so that I can get a 1x3 matrix in the end? Thanks. I think I found it.

Answer
Go into Excel and click on 'Help'. In the input box, type "multiply matrices". You will be shown a number of functions that multiply matrices! :)



Question
Can someone give me an example of a 3x3 matrices times a 3x2?
I'm doing Algebra 2 homework and it's over Multiplying Matrices. The problem I'm stuck on is a 3x3 times a 3x2. I don't wanna say the exact problem bc I want to learn how to do this actually. But could someone make up a problem with the same matrices and show how to solve it? I hope that makes sense. Thanks :) Oh and could you give detailed directions how to solve it please? I mean like step by step. Thanks again :)

Answer
http://www.algebralab.org/lessons/lesson.aspx?file=algebra_matrices_multiplying.xml



Question
What is the largest determinant of a 3x3 matrix using only single-digit numbers?
What is the largest determinant of a 3x3 matrix using only single-digit numbers? This can go by negative or positive numbers, so it's based on magnitude, not actual value.

Answer
By single-digit numbers, do you mean that the entries come from the set {0,1,2,3,4,5,6,7,8,9}? If so, then the maximum determinant is 1458. This the determinant of the matrix [0 9 9; 9 0 9; 9 9 0]. I wrote a computer program to try all combinations, using symmetry to cut down on the search space. EDIT: It just occurred to me that every entry must be 0 or 9. If you fix the other eight entries, then the determinant is a linear function of the ninth entry, and the maximum value of a linear function occurs at an endpoint. So we only need to find the maximum determinant of a matrix of 0's and 1's, and multiply it by 9^3. The maximum determinant of an n by n matrix of 0's and 1's is given by the following sequence: http://www.research.att.com/~njas/sequences/A003432




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