Linear Equation

• Jan 18th 2014, 08:55 AM
Jason76
Linear Equation
Definiton of a linear equation

$a_{1} x_{1} + a_{2}x_{2}... a_{n}x_{n} = b$ where $b$ is a real number

Note if $b = 0$, it's a homogeneous equation.

What are some reasons why these statements are true?

$3x - 4xy = 0$ - not linear

$x^{2} + y^{2} = 4$ - not linear

$(\sin2x) - y = 14$ linear
• Jan 18th 2014, 10:16 AM
HallsofIvy
Re: Linear Equation
Quote:

Originally Posted by Jason76
Definiton of a linear equation

$a_{1} x_{1} + a_{2}x_{2}... a_{n}x_{n} = b$ where $b$ is a real number

Note if $b = 0$, it's a homogeneous equation.

What are some reasons why these statements are true?

$3x - 4xy = 0$ - not linear

the "xy" term cannot be written in the form "ax+ by" for any numbers a and b.

Quote:

$x^{2} + y^{2} = 4$ - not linear

The terms $x^2$ and $y^2$ cannot be written in the form "ax+ by" for any numbers a and b.

Quote:

$(\sin2x) - y = 14$ linear
sin(2x) cannot be written in the form "ax+ by" for any numbers a and b.