Question

Let S = {A, B, C, D} be some set of four elements of a vector space. Suppose that D = 2A + B + 3C and C = A − B. Is {A, B, D} linearly dependent? Explain.

Answer 1

Answer:

As explained

Step-by-step explanation:

given that D = 2A + B + 3C and S = {A, B, C, D}, C = A − B

for {A, B, D}  to be linearly dependent implies that A B and D will have values that not dependent on the sample space C.

if C = A -B is substituted in the original equation, the generated equation, 5A -2B will have values each as against C which is linearly independent.

Also, D will have values that are linearly dependent.