Linear Systems by Matrix

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

• dependent system

• inconsistent system

• equal matrices

• system of equations

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

Write the augmented matrix for the system of linear equations.

2w – 3x + 4z = –12

–3w + 6y – 9z = 7

–x + 4y – 5z = 2

w + 6x + 4y = –9

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Write the augmented matrix for the system of linear equations.

4x + 3y – z = –10

–2x – y + 5z = 24

–3x + 2y – 6z = –11

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Solve the systems of equations by using matrix equations.

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When solving for C in the equation CD=E using inverse matrices, you use the equation:

• C=D^-1E

• C=ED^-1

• C=E^-1D

• C=DE^-1

Which of the following shows the system of equations using a matrix equation?

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Which matrix equation represents this system of equations?

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_____________ is an algorithm to solve a system of linear equations by representing it as an augmented matrix, reducing it using row operations, and expressing the system in reduced row-echelon form to find the values of the variables.

• Gauss-Jordan Reduction Theory

• Gauss-Jordan Reduction Principle

• Gauss-Jordan Law

• Gauss-Jordan Reduction Method