Question

Exercise #4 Use the Gauss-Jordan method to invert the following matrices (if an inverse exists!) by hand. Show your steps! Then check your answer by a) multiplying the original matrix by the inverse, and b) finding the inverse using a Python function. You can do check a) in Python rather than by hand, if you'd prefer.

A) 4 ∣ 3 ∣ 6
6 ∣ 2 ∣ 4
3 ∣ 3 ∣ 3

B) -3 ∣ -5 ∣ 1
9 ∣ 14 ∣ 1
18 ∣ 29 ∣ -2

Answer 1

To invert a matrix using the Gauss-Jordan method, perform row operations to get an identity matrix on the left side and the inverse matrix on the right side.

Step-by-step explanation:

To invert the given matrices using the Gauss-Jordan method, we need to perform row operations until we get an identity matrix on the left side and the inverse matrix on the right side. Let's solve part A:

1. Write the given matrix: A = [[4, 3, 6], [6, 2, 4], [3, 3, 3]].
2. Add the identity matrix on the right side: [4, 3, 6 | 1, 0, 0], [6, 2, 4 | 0, 1, 0], [3, 3, 3 | 0, 0, 1].
3. Perform row operations to get leading 1's and zeros below and above them. After performing the operations, the left side should be transformed into an identity matrix and the right side into the inverse matrix.

We can check the answer using Python by multiplying the original matrix by the computed inverse matrix.