Question

Aljabar Linear
Tolong jawab 1a dan 1b dong

Answer 1

1a

There exists a, b, c ≠ 0 such that

One of them is, a = -2, b = -1, c = 1

This shows that the given set of vectors are linearly dependent hence not a basis of the vector space

1b

Set the two vectors into the form of 3 x 2 Row-Echelon matrix (picture above)

We get that there's only 2 pivot colums which shows that the dimension of the matrix is 2, instead of 3.

This clearly shows that the given set of vectors don't span the space hence not a basis of the vector space