This is really easy, but there is one big thing to remember:
THE SIZES MUST BE THE SAME!
Check it out:
Let's add these guys:
We just add the entries in each spot.
That's it! So, what do ya think - easiest thing on the whole site?
Here's a subtraction guy
Remember that a trinomial has three terms.
Like this guy:
Right now, we're really interested in a certain type of trinomial.
Remember FOIL?
We can multiply
and get
Hey - that's our trinomial from above.
Basically, we'll be figuring out how to "undo" guys
This is a pretty easy method. But, it only works when you can factor
something. As I told you before, except for in math books, things
usually don't factor.
But, this is a good method to help you understand what's going on. so,
here we go!
We're going to
Let's start with an easy one:
Solve
x = 10
We can just look at it and see that
.
But, what if we didn't see that? What would we do?
Here's the Algebra trick:
We'll add
3 to both sides!
*Remember the see saw?
Whatever we do to one side of the equation,
we
Square Roots:
Here are a few square roots:
The first two popped cleanly (because they had perfect squares inside.)
But, the last guy didn't. He's an irrational number. His decimal part
goes on forever and ever and never repeats.
Just like
!
The reason I u
So far, we've learned how to add and subtract matrices (the sizes had to
be the same) and how to multiply a matrix by a scalar. These were really
easy.
Multiplying two matrices is a bit tricky, but, once you get the hang of it,
it's a snap - you just need
Now, we're going to learn how to factor guys with a number in front of
the
.
I'm not going to lie to you - these can be pretty tricky. Some students
don't like these because there is no way to just memorize how to do
them. Each problem is different and yo
Remember from your arithmetic days (or is that daze?) what this
means?
That's three 2's all multiplied together:
As you know by now, in algebra, we work with that unknown guy. Mr. X!
The thing to remember is that x is a number - we just don't know which
o
Remember that monomials are single term critters:
Dividing by these things pops up fairly often in later math classes.
Let's just do one:
Let's rewrite it like this:
Since there is only one term down here, we can break this thing up.
Here's another one:
T
You've already seen glimpses of matrices - determinants (for Cramer's
Rule) and Gaussian elimination. Now, we'll see what else we can do
with them.
A matrix is just a rectangular grid of numbers. Keanu Reeves will tell
you otherwise, but don't believe him