Write your two sets of numbers. To multiply the sets, you work across the first row and down the first column. Multiply each set of numbers and add the products. So if you are combining a 3 x 2 matrix with a 2 x 3 matrix:
[1 2 3] x [a b]
[4 5 6] x [c d]
_______ [e f]
your first set of operations gives you:
[1a + 2c + 3e ____________ ]
[__________ _____________ ]
for the first number in your solution matrix. Multiply row one with column one and add the three products to get your first answer.
Multiply the first row with the second column to find the next number in your solution. The next number will go in the top right corner of the solution matrix:
[1 2 3] x [a b]
[4 5 6] x [c d]
_______ [e f]
your second set of operations gives you:
[___________ 1b + 2d + 3f ]
[___________ __________ ]
Multiply the second row with the first column to find the next number in your solution. The next number will go in the bottom left corner of the solution matrix:
[1 2 3] x [a b]
[4 5 6] x [c d]
_______ [e f]
your third set of operations gives you:
[__________ ___________ ]
[ 4a + 5c + 6e __________ ]
Multiply the second row with the second column to find the last number in your solution. The last number will go in the bottom right corner of the solution matrix:
[1 2 3] x [a b]
[4 5 6] x [c d]
_______ [e f]
your last set of operations gives you:
[_________ __________ ]
[__________ 4b + 5d + 6f]
Write your two sets of numbers. Each set must have the same number of rows and columns:
[1 2 3] + [a b c]
[4 5 6] + [d e f]
Add each set of numbers starting in the top left corner for addition of matrices:
[1+a 2+b 3+c]
[4+d 5+e 6+f]
Subtract each set of numbers starting in the top left corner for subtraction of matrices:
[1-a 2-b 3-c]
[4-d 5-e 6-f]