SCC121 Fundamentals of Computer Science - Linear Equations

Flashcards about Linear equations

Linear Algebra Foundation

Machine learning algorithms, computer graphics, natural language processing, linear programming models, and electrical networks simulations.

Algebra according to Al‐Khwārizmī

An Arabic word meaning 'The science of Equations and Balancing', it's the simplest equation ax = b, with a, b constants, x variable.

Equations

Statements that two expressions are equal.

Linear Equations

Equations in which each variable is raised to the power of 1 (not higher) and without product of variables.

Solving linear equation in one variable

Finding the value for the variable, for which the equation becomes a true statement.

Addition property of equality

If 𝐴 = 𝐵, then 𝐴 + 𝑐 = 𝐵 + 𝑐

Subtraction property of equality

If 𝐴 = 𝐵, then 𝐴 − 𝑐 = 𝐵 − 𝑐

Multiplication property of equality

If 𝐴 = 𝐵, then 𝑐𝐴 = 𝑐𝐵

Division property of equality

If 𝐴 = 𝐵, then 𝐴/𝑐 = 𝐵/𝑐

Equivalent Equations

Equations that have the same solution.

Solving linear equations in two variables

Finding the value for each variable (an ordered pair), for which the equation becomes a true statement.

Cartesian Plane

2D generalization of the number line: ℝ2, with a horizontal (x) and vertical (y) axis. Each point is an ordered pairs of numbers: Point (𝑥, 𝑦). Point (0, 0): the origin of the Cartesian plane

Slope-intercept form

𝑦 = 𝑚 ∙ 𝑥 + 𝑟, where 𝑚 is the slope and 𝑟 is the 𝑦-intercept

Slope

The rate of change

Y-intercept

𝑦 coordinate of the point at which the line crosses the 𝑦 axis

Solving linear equations in three variables

Finding the value for each variable (an ordered 3-tuple), for which the equation becomes a true statement.

3D Space

A generalization of the 2D Cartesian plane: ℝ3 with three orthogonal axes: x, y and 𝑧. Each point is an ordered 3 tuple of numbers: Point (x, y, z). Point (0, 0, 0): the origin of the 3D space