Gauss Elimination

Why we need to use Gauss Elimination for solving linear system of equation

• Gauss Elimination is direct method

• Easy to use

• solving a large system

• accurate

What is an appropriate first row command to solve this by Gaussian Elimination?

• 2R2 + R2 -> R2

• -2R1 + R2 -> R2

• R3 +R2 --> R3

• 2R1 + R2 --> R2

Aina 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

Which of the following is the correct representation for the system of equations?

• A

• B

• C

• D

Farah solved the matrix on the left. Ibrahim solved the matrix on the right. Who is correct?

• Farah, because she multiplied by the reciprocal.

• Ibrahim, because he got the top left number to be a one.

• Neither. They needed to take care of the one and make it a zero first.

• Both. Each step is legal and takes care of the top left term

This is an example of a

• System of Quadratic Equations

• Reduced Row Echelon Form

• Augmented Matrix

• A Canine Doing a Backflip

Ammar wrote a matrix to represent his system of equations. What was his mistake

• The z's are not aligned correctly

• There should be a one in the top row for zero

• There should be a zero in the second column of the third representing the y

• Nothing. This is correct.

In the process of solving a real-world problem involving the optimization of resources in a school project, Chengyuan and Lu are using the Gauss elimination method. Which of the following operations is not allowed?

• Multiplying a row by a nonzero scalar

• Adding a row to another row

• Swapping two rows

• Dividing a row by zero

Imagine Guan, Lu, and Jiaxin are working on a project that involves solving a system of linear equations to optimize the logistics for their supply chain. They decide to use the Gauss elimination method. What is the purpose of scaling rows in this context?

• To make the matrix symmetric

• To ensure that all the diagonal elements are 1

• To reduce computational errors

• To increase the speed of convergence

Imagine Wang is solving a system of linear equations using Gauss elimination in his engineering class. Which of the following is true about the back substitution method he uses after applying Gauss elimination?

• It starts with the first equation and moves downwards

• It can only be used if the matrix is symmetric

• It involves solving for variables starting from the bottom-most equation

• It requires the matrix to be in lower triangular form