Question

Assume u4 is not a linear combination of {u1,u2,u3}

Answer 1

Answer:

A. {u1,u2,u3,u4} is a linearly independent set of vectors unless one of {u1,u2,u3} is the zero vector.

Step-by-step explanation:

Given that u4 is not a linear combination of {u1,u2,u3}

This means there is no possibility to write u4 = au1+bu2+cu3 for three scalars a,b,and c.

This gives that $u_4-au_1-bu_2-cu_3 \neq 0$

This implies that these four vectors are not linearly dependent but linearly independent.

Hence option a is right.

A. {u1,u2,u3,u4} is a linearly independent set of vectors unless one of {u1,u2,u3} is the zero vector.