Variable Systems of Equations with Matrices

A rectangular array of numbers arranged in rows and columns

• system of equations

• matrix

• linear programming

• ordered triples

What is
Cramer's Rule?

• A square matrix that, when multiplied by another matrix, equals that same matrix. If A is any n X n matrix and I is the n X n identity matrix, then A ⋅ I = A and I ⋅ A  =  A.

•  A matrix that contains only the coefficients of a system of equations.

•  A method that uses determinants to solve a system of linear equations.

• A method of solving a system of equations in which one equation is solved for one variable in terms of the other.

What is a
Coefficient Matrix?

• A matrix that contains only the coefficients of a system of equations.

• A square matrix that, when multiplied by another matrix, equals that same matrix. If A is any n X n matrix and I is the n X n identity matrix, then A ⋅ I = A and I ⋅ A  =  A.

• Two n X n matrices whose product is the identity matrix.

• A matrix that contains the constants of a system.

What is a
Variable Matrix?

• A matrix that contains only the coefficients of a system of equations.

•  A matrix that contains the constants of a system.

• A matrix that only contains the variables of a system of equations.

• Two n X n matrices whose product is the identity matrix.

Solve the system.

• (1, 2, -2)

• (1, -3, -2)

• (-1, 3, 2)

• No Solution

Solve the system.

• (3, -2, 4)

• (2, -3, 1)

• (-3, 2, -1)

• Infinitely many solutions

Solve the system. 

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution

Solve the system.

• (2, -2, 3)

• (2, 1, 4)

• (-2, 2, -3)

• No Solution

Find the inverse.

• A

• B

• C

• D

Solve the system of equations to find the value of y.

• -2

• 3

• -3

• 2