SOLUTION: Multiplying matrics [4 1 0 2] 1 0 1 2 -1 0 3 5 1 1 3 0

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Question 292657: Multiplying matrics
[4 1 0 2] 1 0 1
2 -1 0
3 5 1
1 3 0
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
See this solver for more help with multiplying matrices.

Since the first matrix is a 1 by 4 matrix and the second matrix is a 4 by 3 matrix, this means that the resulting matrix will be a 1 by 3 matrix. The final matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.

So the final resulting matrix will look like:


%28matrix%281%2C3%2Cx%2Cx%2Cx%29%29


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



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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:



So the element in the 1st row, 1st column of the resulting matrix is 8. Now let's update the matrix:

%28matrix%281%2C3%2C8%2Cx%2Cx%29%29
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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:



So the element in the 1st row, 2nd column of the resulting matrix is 5. Now let's update the matrix:

%28matrix%281%2C3%2C8%2C5%2Cx%29%29
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Multiply the corresponding entries from the 1st row of the first matrix by the 3rd column of the second matrix. After multiplying, add the values:


1st row, 3rd column:



So the element in the 1st row, 3rd column of the resulting matrix is 4. Now let's update the matrix:

%28matrix%281%2C3%2C8%2C5%2C4%29%29








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Answer:


So the solution is %28matrix%281%2C3%2C8%2C5%2C4%29%29

In other words,



Once again, see this solver for more help with multiplying matrices.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

This is a red%281%29xgreen%284%29 matrix multiplied by a green%284%29xred%283%29.
The multiplication is defined because the two (green) inner
dimensions are both green%284%29 and the product matrix will
have the outer (red) dimensions red%281%29xred%283%29.
So we make a blank 1x3 matrix to fill in:

The first element to fill in is the 1st (only) row and 1st column.
So we multiply the first (only) row of the first matrix by the
first column of the second matrix and then add them like this:
4%2A1+%2B+1%2A2+%2B+0%2A3+%2B+2%2A1+=+4+%2B+2+%2B+0+%2B+2+=+8, so
we put red%288%29 in the first blank of the product matrix:

The second element to fill in is the 1st (only) row and 2nd column.
So we multiply the first (only) row of the first matrix by the
2nd column of the second matrix and then add them like this:
4%2A0+%2B+1%2A%28-1%29+%2B+0%2A5+%2B+2%2A3+=+0+-+1+%2B+0+%2B+6+=+5, so
we put red%285%29 in the second blank of the product matrix:


The third element to fill in is the 1st (only) row and 3rd column.
So we multiply the first (only) row of the first matrix by the
3rd column of the second matrix and then add them like this:
4%2A1+%2B+1%2A0+%2B+0%2A1+%2B+2%2A0+=+4+%2B+0+%2B+0+%2B+0+=+4, so
we put red%284%29 in the third blank of the product matrix: