Label the following statements as true or false. (a) The zero vector is a linear

Problem 1

Label the following statements as true or false

(a) The zero vector is a linear combination of any non – empty set of vectors

(b) The span of is

(c) If S is a subset of a vector space V, then span(S) equals the intersection of all subspaces of V that contain S

(d) In solving a system of linear equations, it is permissible to multiply an equation by any constant

(e) In solving a system of linear equations, it is permissible to add any multiple of one equation to another

(f) Every system of linear equations has a solution

                                                              Step by Step Solution

Step 1 of 6

(a) Given statement is:

The zero vector is a linear combination of any non – empty set of vectors.

This statement is true because for any non – empty set of vectors , the vector 0 can be expressed as

            (i)

If , then equation (i) holds and the statement is true.

, then we can choose  such that equation (i) holds and in that case, the statement is also true