Solving Systems by Gaussian Elimination

This is an example of a

• System of Quadratic Equations

• Reduced Row Echelon Form

• Augmented Matrix

• A Canine Doing a Backflip

This is an example of

• Row Echelon Form

• Reduced Row Echelon Form

• Really Reduced Echelon Form

• Really Really Easy Form

Reduced Row Echelon Form is where ______________________

• Zeroes in the first column of my matrix

• Thel ast column has all zeroes

• One's are in a diagonal pattern of my matrix with zeroes underneath the one's.before the augmented portion

• One's are in a diagonal pattern of my matrix with zeroes above and below the ones before the augmented portion

What is the solution to the 4x5 Matrix?

• ( 3, 4, 9, 6 )

• ( 3, 4, 9, -6 )

• ( -6, 9, 4, 3 )

• ( 6, 9, 4, 3 )

What is the solution to the systems of equations represented by the 3x4 Matrix?

• (4, 6, 2)

• (-6, 2, 2)

• All Real Numbers

• No Solutions

• (2,3,5,0)

• (2,3,4,5)

• All Real Numbers

• No Solution

Using back-substitution, calculate the solution for the REF matrix.

• (3, -6, 3)

• (-6, -6, 3)

• (6, -6, 3)

• (-6, -6, 3)

Back-substitute to calculate the solution from the REF Matrix.

• 2, 4, (1/2)

• (-1/5), 4, (1/2)

• (1/2), 2, 1

• (1/5) , 4, (1/2)

Johnny was using Gaussian Elimination to simplify the matrix. What did he do wrong in this step?

• To get a zero for a number you should multiply the same row by its' reciprocal

• If you multiply a number to a row you have to change that row too

• He added the numbers incorrectly

• Nothing. This step was correct.

Jessica is simplifying the matrix using Gaussian Elimination. Did she complete the step correctly?

• No, she should have changed the 2 to a zero and multiplied -2 by R2 and added R1

• No, she wanted to change the 3 to a zero so she should have multiplied R2 and added it to R3

• Yes. When you need a zero you multiply by the number's reciprocal.

• No. Just punch in the calculator. Who cares about Carl Gauss