MathAlgebraLinear algebraMatrices

Matrix inverse properties

Unique solutions and invertibility

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Suppose you are analyzing a square system $A \mathbf{x}=\mathbf{b}$ .

If you find that there is a unique solution for any non-zero vector $\mathbf{b}$ , then can you affirm that $A$ is invertible?

Select one option from the list

Yes, because the solutions are unique

No, because the system cannot be square

Yes, because

\mathbf{b}

isn't the zero vector

No, because you cannot ensure that the system

A \mathbf{x}=\mathbf{0}

has a unique solution

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