Question

consider the following two systems. (a) (b) (i) find the inverse of the (common) coefficient matrix of the two systems.

Answer 1

To find the inverse of a coefficient matrix, perform row operations on the matrix until it becomes the identity matrix; the resulting augmented matrix on the right will be the inverse.

Step-by-step explanation:

Since the actual equations of the systems are not provided in the question, we cannot calculate the inverse of the coefficient matrix directly here. However, to find the inverse of a matrix you generally perform the following steps:

1. Write the matrix and the identity matrix side by side as an augmented matrix.
2. Perform row operations to turn the original matrix into the identity matrix.
3. The transformations that turned the original matrix into the identity matrix will conversely turn the identity into the inverse matrix.
4. Once you have the identity matrix on the left, the matrix on the right of the augmentation will be the inverse matrix.

Remember, a matrix has an inverse only if it is square (same number of columns and rows) and its determinant is non-zero.