Question

Describe geometrically (line, plane, or all of r 3) all linear combinations of

Answer 1

Step-by-step explanation:

 If all vectors are a multiple of each other, they form a line through the origin. If 2 vectors are independent, that is, not a multiple of each other, they "span" a plane. If 3 vectors are independent, that is, the 3rd can not be written as the sum of multiples of the other 2 vectors, they "span" all of R3.

Answer 2

Step-by-step explanation:

Suppose, all vectors are multiple to each other then, they make a line within the origin.

If two vectors are independent of each other, they "span" a plane.

If three vectors are not dependent on each other then the 3rd can not be written as the sum of multiples of the other 2 vectors, they "span" all of R3.

If the third vector is written as the sum of multiples of the other 2 vectors, then that vector belongs to the plane those 2 vectors "span".