Question

Solve the following systems of equations using the matrix method shown in class

3*x1 + x2 + 5*x3 = 20
-x1 + 4* x2 = 0
2*x1 + 3*X2 - x3 = 7

Answer 1

To solve the given system of equations using the matrix method, we need to represent the system in matrix form and then perform row operations to transform the matrix into reduced row-echelon form.

Step-by-step explanation:

To solve the given system of equations using the matrix method, we need to represent the system in matrix form and then perform row operations to transform the matrix into reduced row-echelon form.

Step-by-Step Solution:

1. Write the system of equations in matrix form:

• [3, 1, 5][x1, x2, x3] = [20]
• [-1, 4, 0][x1, x2, x3] = [0]
• [2, 3, -1][x1, x2, x3] = [7]

Create the augmented matrix:

• [3, 1, 5, 20]
• [-1, 4, 0, 0]
• [2, 3, -1, 7]

Perform row operations to transform the augmented matrix into reduced row-echelon form:

• Use row operations to create zeros below the leading entry in the first column:
• Use row operations to create zeros above the leading entry in the second column:
• Use row operations to create a leading entry of 1 in each row:
• Use row operations to create zeros above and below each leading 1:

The matrix is now in reduced row-echelon form.Extract the solution from the matrix:

• x1 = 4.5
• x2 = 1.5
• x3 = -3

Therefore, the solution to the given system of equations is x1 = 4.5, x2 = 1.5, and x3 = -3.