Solving System of Equations Matrix

Solve the following system of equations.

• (-7, -5)

• (-7, -9)

• (7, -9)

• (-7, 5)

Solve the following systems of equations.

-x+6y-z=6

2x+y-3z=16

-x+5y+3z=-7

• A (0, -6, 0)

• B (0, 0, -6)

• C (3, 1, -3)

• D (-6, 4, -3)

Solving Systems:
Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Two or more equations with two or more of the same variables

• dependent system

• inconsistent system

• equal matrices

• system of equations

A rectangular array of numbers arranged in rows and columns

• system of equations

• matrix

• linear programming

• ordered triples

When solving a system AX=B using inverse matrices, you use the equation:

• X=A^-1B

• B=X^-1A

• A=X^-1B

• X=B^-1A

Systems of 3 Equations:
-x+6y-z=6
2x+y-3z=16
-x+5y+3z=-7

• (0, -6, 0)

• (0, 0, -6)

• (3, 1, -3)

• (-6, 4, -3)

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 are
Inverse Matrices?

• A matrix that contains the constants of a system.

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

• A square array of numbers or variables enclosed between two parallel lines.

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