Answer the following questions about the role of the determinant in solving a system of linear equations:
(a) Define a singular matrix and state the condition on its determinant.
(b) Consider the matrix equation AX=B. Explain, without performing any calculations, why the system cannot have a unique solution when A is singular.
(c) Give a brief justification of how the condition ∣A∣=0 guarantees a unique solution for the system AX=B. Mention the relevant matrix that becomes available when ∣A∣=0.