Solve each system, using the method indicated.
x - z = -3
y + z = 6
2x - 3z = -9
(Gauss-Jordan)
Verified step by step guidance
1
Write the system of equations in augmented matrix form: .
Use row operations to get a leading 1 in the first row, first column (which is already done).
Eliminate the first column below the leading 1 by replacing Row 3 with Row 3 minus 2 times Row 1: .
Next, eliminate the third column in the second row by replacing Row 2 with Row 2 plus Row 1: .
Continue using row operations to achieve reduced row-echelon form, ensuring each leading entry is 1 and all other entries in its column are 0.
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
7m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Systems of Equations
A system of equations consists of two or more equations with the same set of variables. The goal is to find values for the variables that satisfy all equations simultaneously. In this case, the system includes three equations with three variables: x, y, and z.
Gauss-Jordan elimination is a method for solving systems of linear equations by transforming the system's augmented matrix into reduced row echelon form. This process involves using row operations to simplify the matrix, making it easier to identify the values of the variables directly.
An augmented matrix is a matrix that represents a system of linear equations, including the coefficients of the variables and the constants from the equations. It is formed by appending the constant terms as an additional column to the coefficient matrix, facilitating the application of elimination methods like Gauss-Jordan.