Let B be the set....

Question

Let B be the set....

|-2 | | 6 |

B = { | 3 | , | -1 | }

| 0 | | 5 |

Determine if B is a basis for R^3 and check the correct answer(s) below.

A.  B is not a basis because it does not span 

B.  B is a basis.

C. B is not a basis because it is not a linearly independent set.

Answer 1

The set of vectors shown is not a basis because it only has 2 vectors. A basis for R³ has to have 3 vectors. So it does not span, so answer A is the correct answer.

Answer B is not correct because it is not a basis.

Answer C, while correctly stating it is not a basis, the vectors are actually independent.

Robert Clark