Question

A system of linear equations is represented as AX = B, where A is variable matrix and B is the constant matrix. Then the system of equations is ______.

Options

• Consistent, if |A| ≠ 0, solution is given by X = BA⁻¹

• Inconsistent if |A| = 0 and (adj A) B = 0

• Inconsistent if |A| ≠ 0

• May or may not be consistent if |A| = 0 and (adj A) B = 0

Answer 1

A system of linear equations is represented as AX = B, where A is variable matrix and B is the constant matrix. Then the system of equations is may or may not be consistent if |A| = 0 and (adj A) B = 0.

Explanation:

AX = B

System of equations is consistent if |A| = 0 and X = A⁻¹B

but may or may not be consistent if |A| = 0 and (adjA).B = 0