SOLUTION: Help! What is an augmented matrix? Give an example based on a system of equations. Thank You!

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Question 151663: Help! What is an augmented matrix? Give an example based on a system of equations. Thank You!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say that we have the system

system%283x%2B2y%2B5z=10%2Cx%2B3y%2B6z=13%2C12x%2B2y%2B4z=14%29


You can write this system in a more compact form by ignoring the variables and focusing on the coefficients like this:

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Note: I simply wrote each coefficient in each element of the matrix. So for the first row I took the coefficients 3,2, and 5 and the value on the right side 10 and wrote them in the first row.


The reason why it's called an "augmented" matrix, is because the original matrix (the left hand matrix) is joined with the right hand column to form a new "augmented" matrix.