Understanding Reduced Row Echelon Form

This video tutorial explains how to transform an augmented matrix into reduced row echelon form to solve systems of equations. It begins with an overview of the conditions for a matrix to be in reduced row echelon form, followed by a detailed explanation of Gaussian elimination. The tutorial includes step-by-step examples of solving both 2x2 and 3x3 systems of equations using these methods. The video concludes with a brief mention of using a graphing calculator to verify solutions.

What is the first condition for a matrix to be in Reduced Row Echelon Form?

• Each column must have a leading entry.

• The first nonzero element in each row is one.

• All elements must be integers.

• All rows must be zero.

Which operation is NOT part of Gaussian Elimination?

• Interchanging two rows.

• Multiplying a row by zero.

• Adding or subtracting rows.

• Multiplying a row by a nonzero number.

In the system of two equations, what is the purpose of replacing Row 1 with 2 * Row 1 plus Row 2?

• To make the first row all zeros.

• To create a zero in the first row's second column.

• To make the second row all ones.

• To create a zero in the second row's first column.

What is the least common multiple used to eliminate the second row's first element in the two equations system?

• 14

• 21

• 7

• 3

In the system of three equations, what is the first step to achieve zeros in the first column of the second and third rows?

• Replace Row 2 with Row 2 plus Row 3.

• Replace Row 2 with -2 * Row 2 plus Row 1.

• Replace Row 1 with Row 2 minus Row 3.

• Replace Row 3 with Row 3 plus Row 1.

What operation is performed to make the second row's second element zero in the three equations system?

• Multiply Row 3 by 2 and subtract from Row 2.

• Multiply Row 2 by -3 and add to Row 1.

• Multiply Row 1 by 3 and add to Row 2.

• Multiply Row 2 by 2 and add to Row 3.

What is the final step to achieve the main diagonal of ones in the three equations system?

• Subtract the rows from each other.

• Divide each row by its leading entry.

• Add the rows together.

• Multiply each row by its leading entry.

After achieving RREF, what is the value of x in the three equations system?

• 2

• -2.5

• 4

• 0

What is the value of y in the three equations system after achieving RREF?

• 4

• -2.5

• -2

• 0

What is the value of z in the three equations system after achieving RREF?

• -2

• 4

• 0

• -2.5