MathAlgebraLinear algebraLinear operators

Null space and range

The existence of solutions

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Here is one more application of the Dimension Theorem.

Let's say you have a $3 \times 5$ system. After doing some work with its matrix $A$ , you discover that the dimension of its null space is equal to $2$ .

What can you say about the system $Ax=b$ ?

Select one option from the list

There isn't enough information to decide

It has a solution for any value of

b

It has a solution only for

b=0

Nothing can be said about the range of

L_A

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