Linear Algebra

A linear function is called "linear" because it represents a straight line.

To graph a linear function, find two points that satisify that function, plot them, and then draw a straight line between them.

START

INPUT a,b,c

d=B*B-4ac

x1=-b+d/2a

x2=-b-d/2a

print x1,x2

stop

If they have the same slope, then there are two possibilities. First say they have the same slope and different y intercepts. This means they are parallel lines and there is no intersection. The solution is the empty set or we say there is no solution.

If the y intercept is the same, then the two equations represent the same line. In this case there is an infinite number of solutions.

A non-linear equation is any equation which includes variables with a degree other than one. Therefore, any equation involving x2, x3, x4, .... would be non-linear.

For example:

y= 3x+2 is linear, because x and y are both degree 1 (no exponent)

y= 2x2 is non-linear, because x is degree 2.

Assuming base-10 logarithms the antilog of 2.068 is 116.95 (to two decimal places).

A linear presentation is a straight line of presentations. (:

The set of points the graphed equations have in common.

This is usually a single point but the lines can be coincident in which case the solution is a line or they can be parallel in which case there are no solutions to represent.

It's anything that doesn't describe the object.

3

y=x+2/4 (x+2 is all over four)

Domain is the number of x values that can be used and not cause an imaginary result.

Range is the number of the y values that result.

In f(x)=2x-5 the range is all real numbers.

y = 0 and x = 8.

It is not always the best method, sometimes elimination is the way you should solve systems. It is best to use substitution when you havea variable isolated on one side

The two numbers are... -36 and -36

A line with no slope is a vertical line. The slope is undefined, and cannot be represented by a real number.

A horizontal line has a slope, but the slope is zero.

Consider the "y = mx + b" form of the straight line equation. For a horizontal line the slope is zero, so y = 0x +b => y = b, which is the equation of a horizontal line. For a vertical line, there is no slope, so you can't substitute for m; the equation can't be written in the form y = mx +b. The equation of a vertical line has the form x = a.

internet

It can by a polynomial of degree 2 or more, eg y = ax4 + bx3 + cx2 + dx + e

Or inverse: y = a/x + b

Or power: y = a*bx

Or trigonometric: y = sin(ax + b)

etc, etc

You could do so many. Here are some examples:

15n=105

15n+105=1005

15n-105=270

Hope this is what you were looking for. :)

Good luck!

The solution of a system of linear equations is a pair of values that make both of the equations true.

Inconsistent.

Elimination and substitution are two methods.

using a calculator.

Linear Equations are equations with variable with power 1

for eg:

5x + 7 = 0

Simultaneous Equations are two equations with more than one variable so that solving them simultaneously

The magnitude of dot product of two vectors is equal to the product of first vector to the component of second vector in the direction of first.

for ex.- A.B=ABcos@