SOLUTION: how do I solve the equation by multiplying: AB A=(3, 0, 2, -1) B=(2, 8, .6, 3)

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Question 176528: how do I solve the equation by multiplying: AB A=(3, 0, 2, -1) B=(2, 8, .6, 3)
Found 2 solutions by heidi_dommer, jim_thompson5910:
Answer by heidi_dommer(1) About Me  (Show Source):
Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!
I'll assume that the matrices really look like:

A=%28matrix%282%2C2%2C3%2C0%2C2%2C-1%29%29 and B=%28matrix%282%2C2%2C2%2C8%2C0.6%2C3%29%29


AB Start with the given expression.


%28matrix%282%2C2%2C3%2C0%2C2%2C-1%29%29%28matrix%282%2C2%2C2%2C8%2C0.6%2C3%29%29 Plug in A=%28matrix%282%2C2%2C3%2C0%2C2%2C-1%29%29 and B=%28matrix%282%2C2%2C2%2C8%2C0.6%2C3%29%29


Since the first matrix is a 2 by 2 matrix and the second matrix is a 2 by 2 matrix, this means that the resulting matrix will be a 2 by 2 matrix.

So the final resulting matrix will look like:


%28matrix%282%2C2%2Cx%2Cx%2Cx%2Cx%29%29


note: the "x"s are just placeholders for now





Multiply the corresponding entries from the 1st row of the first matrix by the 1st column of the second matrix. After multiplying, add the values:
1st row, 1st column:
%283%29%2A%282%29%2B%280%29%2A%280.6%29=6%2B0=6


So the element in the 1st row, 1st column of the resulting matrix is 6. Now let's update the matrix:

%28matrix%282%2C2%2C6%2Cx%2Cx%2Cx%29%29
--------------------------------------------------




Multiply the corresponding entries from the 1st row of the first matrix by the 2nd column of the second matrix. After multiplying, add the values:
1st row, 2nd column:
%283%29%2A%288%29%2B%280%29%2A%283%29=24%2B0=24


So the element in the 1st row, 2nd column of the resulting matrix is 24. Now let's update the matrix:

%28matrix%282%2C2%2C6%2C24%2Cx%2Cx%29%29
--------------------------------------------------


================================================================================




Multiply the corresponding entries from the 2nd row of the first matrix by the 1st column of the second matrix. After multiplying, add the values:
2nd row, 1st column:
%282%29%2A%282%29%2B%28-1%29%2A%280.6%29=4%2B-0.6=3.4


So the element in the 2nd row, 1st column of the resulting matrix is 3.4. Now let's update the matrix:

%28matrix%282%2C2%2C6%2C24%2C3.4%2Cx%29%29
--------------------------------------------------




Multiply the corresponding entries from the 2nd row of the first matrix by the 2nd column of the second matrix. After multiplying, add the values:
2nd row, 2nd column:
%282%29%2A%288%29%2B%28-1%29%2A%283%29=16%2B-3=13


So the element in the 2nd row, 2nd column of the resulting matrix is 13. Now let's update the matrix:

%28matrix%282%2C2%2C6%2C24%2C3.4%2C13%29%29
--------------------------------------------------






==============================================================================


Answer:


So the solution is %28matrix%282%2C2%2C6%2C24%2C3.4%2C13%29%29

In other words,





So AB=%28matrix%282%2C2%2C6%2C24%2C3.4%2C13%29%29