Question

r4=r1+r2=r3,which of the vectors are linearly dependent?
a)r1
b)r3
c)r4
d)r2m

Answer 1

Answer on Question #59688 – Math – Linear Algebra

Question

r4=r1+r2=r3. which of the vectors are linearly dependent?

a) r1

b) r3

c) r4

d) r2

Solution

$$r1+r2=r3$$ $$r1+r2=r4$$

By definition, vectors $X_1, X_2, X_3$ are linearly dependent if there exist constants $c_1, c_2, c_3$ not all zero, such that

$$c_1 X_1 + c_2 X_2 + c_3 X_3 = 0$$

Vector $r_4$ is linearly dependent. Vector $r_3$ is linearly dependent too. Thus, the correct answers are b) and c).

Answer: b) r3 and c) r4.

www.AssignmentExpert.com