Question

A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is

Options

• ‘A’ must be invertible

• ‘b’ must be linearly depended on the columns of A

• ‘b’ must be linearly independent of the columns of A

• None of these

Answer 1

‘A’ must be invertible

Explanation:

For a set of linear equations, Ax = b.

The inverse of matrix A exists (i.e. |A| ≠ 0). This is the necessary condition for the existence of a solution for this system.