Use matrices to solve systems of linear equations. Augmented matrix reduction.

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Determinant for matrix 2x2:

matrix

has determinant

 
Determiant for matrix 3x3:

matrix

       

has determinant

 

Equivalent system:  A system of equations having the same solution set as another system.

Graph of an equation in two variables:  All the points that may be graph from the solution set of the equation.

Graph of a function:  The solution set graphed for the function in the given domain.

Graph of a number:   The location of a point paired with a number in the number line.

Graph of an ordered pair:  The location in the coordinate plane associated with an ordered pair of real numbers.

Linear equation:   Any equation with all exponents = 1 regardless of the form the equation is represented.

Linear equation in two variables:   All equivalent equations to the one in the form of ax + by = c, where a, b, and c are in the set of the real numbers and a and b can't be zero at the same time. The graph is a straight line.

Linear function:  A function of the form: f(x) = mx + b.

Matrix: Rectangular arrangement of numbers in rows and columns that uses large brackets in order to define the matrix. A matrix size is defined by number of rows and number of columns.

Ordered pair:   In a coordinate plane is the location of a point.

Point-slope form of an equation:  y - y1 = m(x-x1), where m is the slope and (x1 , y1) the point for which the line goes through.

Slope of a line:The measure of how steep a line is. The change in y (rise) divided by the change in x (run). Slope = m

Slope-intercept form of an equation:   The equation of a line in the form y = mx + b, where m represents the slope, and be represents the y-intercept.

Solution of an equation in two variables:  Any ordered pair of real numbers that makes the sentence true.

Solution of a system of two equations in two variables:   Ordered pair that when replaced in the equations produces a true statement for both equations.

Solve a system of two equations in x and y:   Finding all ordered pairs (x,y) which make both equations in the system true.

Standard form of a linear equation:   ax + by = c, where a, b, and c are integers and a and b are not both zero.

 

 
 
 
       

 

   

 
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