SOLUTION: Solve: If A= [2 3] and B = [0 -2], find AB. [1 4] [1 5] the 1 and 4 are under 2 and 3, the 1 and 5 are under 0 and -2.

Algebra.Com
Question 636414: Solve: If A= [2 3] and B = [0 -2], find AB.
[1 4] [1 5]
the 1 and 4 are under 2 and 3, the 1 and 5 are under 0 and -2.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
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. 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%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: %28matrix%282%2C2%2Chighlight%282%29%2Chighlight%283%29%2C1%2C4%29%29%28matrix%282%2C2%2Chighlight%280%29%2C-2%2Chighlight%281%29%2C5%29%29

%282%29%2A%280%29%2B%283%29%2A%281%29=0%2B3=3



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



%28matrix%282%2C2%2C3%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: %28matrix%282%2C2%2Chighlight%282%29%2Chighlight%283%29%2C1%2C4%29%29%28matrix%282%2C2%2C0%2Chighlight%28-2%29%2C1%2Chighlight%285%29%29%29

%282%29%2A%28-2%29%2B%283%29%2A%285%29=-4%2B15=11



So the element in the 1st row, 2nd column of the resulting matrix is 11. Now let's update the matrix:



%28matrix%282%2C2%2C3%2C11%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: %28matrix%282%2C2%2C2%2C3%2Chighlight%281%29%2Chighlight%284%29%29%29%28matrix%282%2C2%2Chighlight%280%29%2C-2%2Chighlight%281%29%2C5%29%29

%281%29%2A%280%29%2B%284%29%2A%281%29=0%2B4=4



So the element in the 2nd row, 1st column of the resulting matrix is 4. Now let's update the matrix:



%28matrix%282%2C2%2C3%2C11%2C4%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: %28matrix%282%2C2%2C2%2C3%2Chighlight%281%29%2Chighlight%284%29%29%29%28matrix%282%2C2%2C0%2Chighlight%28-2%29%2C1%2Chighlight%285%29%29%29

%281%29%2A%28-2%29%2B%284%29%2A%285%29=-2%2B20=18



So the element in the 2nd row, 2nd column of the resulting matrix is 18. Now let's update the matrix:



%28matrix%282%2C2%2C3%2C11%2C4%2C18%29%29









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



Answer:



So the solution is %28matrix%282%2C2%2C3%2C11%2C4%2C18%29%29





In other words,





%28matrix%282%2C2%2C2%2C3%2C1%2C4%29%29%2A%28matrix%282%2C2%2C0%2C-2%2C1%2C5%29%29=%28matrix%282%2C2%2C3%2C11%2C4%2C18%29%29
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