Question

Solve (if possible) the following systems of linear equations by Gauss-Jordan elimination: a. x+3y=1 x−2y=−4 ​b. x−2y=−5 3x+4y=15 Verify your answers in MatLaB using the commands rref and A \b.

Answer 1

To solve the given systems of linear equations, we can use Gauss-Jordan elimination to reduce the augmented matrix to its row-reduced echelon form (RREF). The first system has a unique solution, x = 2 and y = 1. The second system has infinitely many solutions, with one possible solution being x = 3 and y = -2.

Step-by-step explanation:

To solve the given systems of linear equations using Gauss-Jordan elimination, we can create an augmented matrix and perform a series of row operations to reduce the matrix to its row-reduced echelon form (RREF).

For the first system of equations:

Create the augmented matrix:

[1 3 1 | 1
x -2 -4 | 0]

Perform row operations to obtain the RREF:

[1 0 -2 | 2
0 1 3 | 1]

Therefore, the solution to the first system of equations is x = 2 and y = 1.

For the second system of equations:

Create the augmented matrix:

[1 -2 -5 | 0
3 4 15 | 0]

Perform row operations to obtain the RREF:

[1 0 3 | 0
0 1 -2 | 0]

The second system of equations has infinitely many solutions, with x = 3 and y = -2 being one possible solution.

Learn more about Gauss-Jordan elimination