Final answer:
Two vectors are linearly dependent if and only if they lie on a line through the origin.
Step-by-step explanation:
In mathematics, two vectors are linearly dependent if and only if they lie on the same line through the origin. This means that one vector is a multiple of the other. For example, if vector A is (2, 4) and vector B is (4, 8), then vector B is a scalar multiple of vector A and they are linearly dependent.
However, it is not necessary for two vectors to lie on a line through the origin to be linearly dependent. They can still be linearly dependent if they lie on a line that doesn't pass through the origin. For example, if vector A is (1, 2) and vector B is (3, 6), they are still linearly dependent.
In summary, the statement (t/f) two vectors are linearly dependent if and only if they lie on a line through the origin is false.