Row Echelon Form and Solutions

This video tutorial explains how to use Gauss-Jordan elimination to solve a system of equations with three variables. It begins with setting up the problem and converting it into an augmented matrix. The tutorial then demonstrates various row operations to transform the matrix into reduced row echelon form, ultimately leading to the solution of the variables x, y, and z.

What method is being used to solve the system of equations in this lesson?

• Gaussian Elimination

• Gauss-Jordan Elimination

• Matrix Inversion

• Substitution Method

What is the first step in converting the system of equations into an augmented matrix?

• Add a vertical bar to separate sides

• Multiply the equations by a constant

• Write the coefficients of the variables

• Write the constants on the right side

What operation is performed to make the first element of the second row zero?

• Multiply row 1 by 2 and add to row 2

• Divide row 1 by 2 and subtract from row 2

• Subtract row 1 from row 2

• Add row 1 to row 2

How is the second element of the third row made zero?

• Add row 2 to row 3

• Multiply row 3 by 2 and subtract from row 2

• Subtract row 2 from row 3

• Multiply row 2 by 2 and add to row 3

What is the final step to achieve reduced row echelon form?

• Swap rows to achieve identity matrix

• Make all off-diagonal elements zero

• Multiply entire matrix by a constant

• Make all diagonal elements one

What is the value of x in the solution?

• 7

• 8

• 6

• 5

What is the value of y in the solution?

• 2

• -1

• 0

• 1

What is the value of z in the solution?

• -3

• 0

• -2

• -1

Which of the following is the correct solution to the system of equations?

• (5, -1, -2)

• (6, 0, -2)

• (6, -1, -2)

• (7, -1, -3)

What is the purpose of achieving reduced row echelon form in solving systems of equations?

• To simplify the equations

• To directly read the solution

• To check for consistency

• To eliminate variables