# Linear Equation

• Jan 18th 2014, 07:55 AM
Jason76
Linear Equation
Definiton of a linear equation

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

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

What are some reasons why these statements are true?

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

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

$\displaystyle (\sin2x) - y = 14$ linear
• Jan 18th 2014, 09:16 AM
HallsofIvy
Re: Linear Equation
Quote:

Originally Posted by Jason76
Definiton of a linear equation

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

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

What are some reasons why these statements are true?

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

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

Quote:

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

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

Quote:

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