TABLE OF CONTENTS
Use these matrices for the example:
We are finding
We multiply the 2 with each entry (e) in the matrix and that gives us our product:
e11 = (2)(2) = 4e12 = (2)(4) = 8e21 = (2)(3) = 6e22 = (2)(4) = 6
Find 2B + C
We are just subbing in our matrices for the variables:
First we find 2B or not to be? Nah, that's not the question. Just 2B, and we do that by multiplying 2 through B entry by entry:
2B = (2)(1) = 2; (2)(5) = 10; (2)(4) = 8; (2)(2) = 4
And we are left with an addition problem:
Naturally we remember that we just add them entry by entry to find the answer:
2 + 0 = 2; 10 + 2 = 12; 8 + 0 = 8; 4 + 1 = 5
2(A + C)
Here we have one number that will be multiplied through two matrices thanks to the distributive property you remember from your Way Back Machine, so this:
ends up being this:
2A + 2C
and as we already know, we just substitute our matrices for the variables and get:
Next we multiply the 2.
At which point we recognize that this is a simple addition of matrices situation and that the entries that correspond with each other in the two matrices get added together:
We tell it to you straight.
It’s not all togas and Solo cups.