Introduction to Matlab

1703 Lecture: Introduction to Matlab

$ x - 2y = 1 $

Can someone give me some values of x and y that satisfy this equation?

x	y
3	1
1	0
2	$ \frac{1}{2} $
101	50

How many combinations of x and y will satisfy this equation? $ \infty $

How else can we represent this equation?

As a line:

(insert figure here)

Is the slope positive or negative?

What's the slope?

$ 3x + 2y = 11 $

Some values of x and y that satisfy this equation?

x	y
3	1
1	4
75

How many combinations of x and y will satisfy this equation? $ \infty $

We can also represent this equation as a line

(insert figure here - both lines on same plot)

What's the slope?

We can see that the point x=3, y=1 is where these two lines meet - which means it is the combination of x and y that satisfies both of these equations.

How else can we represent these equations?

In column form:

$ \left[ \begin{array}{cc} 1 \\ 3 \end{array} \right] x + \left[ \begin{array}{cc} -2 \\ 2 \end{array} \right] y = \left[ \begin{array}{cc} 1 \\ 11 \end{array} \right] $

After pushing these two columns together, we get:

$ \left[ \begin{array}{cc} 1 & -2 \\ 3 & 2 \end{array} \right] \left[ \begin{array}{cc} x \\ y \end{array} \right] = \left[ \begin{array}{cc} 1 \\ 11 \end{array} \right] $