Introduction to Systems of Linear Equations

Front

What is a system of linear equations?

Back

A system of linear equations consists of multiple linear equations that are solved together.

Front

What is the general form of a linear equation in two dimensions?

Back

The general form is ax + by = c, where a and b are not both 0.

Front

What is the general form of a linear equation in three dimensions?

Back

The general form is ax + by + cz = d, where a, b, and c are not all 0.

Front

How is a linear equation in n variables defined?

Back

A linear equation in n variables x1, x2, ..., xn can be expressed as a1x1 + a2x2 + ... + anxn = b, where a1, a2, ..., an and b are constants, and the a's are not all zero.

Front

What is the form of a homogeneous linear equation?

Back

A homogeneous linear equation has the form a1x1 + a2x2 + ... + anxn = 0.

Front

What happens when b = 0 in a linear equation?

Back

The equation becomes a homogeneous linear equation.

Front

What are the special cases for linear equations when n = 2 or n = 3?

Back

For n = 2, the equation is a1x + a2y = b; for n = 3, it is a1x + a2y + a3z = b, where a1, a2 are not both 0 and a1, a2, a3 are not all 0.