I can assist you with solving or explaining the questions in the image. Let me know which question you'd like to start with or if you'd like an explanation for the entire exam! Here’s a brief breakdown of the topics:

1. Matrix Operations:

(a) Checking if a given matrix is singular or non-singular.
(b) The significance of singular matrices and finding the inverse of a matrix.
(c) Solving a system of linear equations using the inverse matrix method.

2. Augmented Matrix and System Consistency:

(a) Defining an augmented matrix for given systems of equations.
(b) Consistency/inconsistency of systems and converting to echelon form.
(c) Checking the consistency of the system and solving if consistent.
(d) Finding the inverse of a matrix using row operations.

3. Rank, Nullity, and Eigenvalues:

(a) Defining rank and nullity, and computing them for a matrix.
(b) Finding eigenvalues of a given matrix.

Let me know which part you'd like to solve or learn about!