3 4 in each of the following determine whether or not

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3 4. In each of the following, determine whether or not X is a basis of R3 . a) X = b) X = c) X = 1 0 3 1 0 3 1 0 3 , , , 2 1 −1 2 1 −1 2 1 −1 , , , 1 −5 4 −1 −2 11 1 −5 4 . . , 1 2 3 . 5. Let f1 (x) = cos x, f2 (x) = cos(x + 1) and f3 (x) = sin x. Show that {f1 , f2 , f3 } is a linearly dependent subset of F. 6. Let Y = {f1 , f2 , f3 }, where f1 (x) = sin x, f2 (x) = sin 3x and f3 (x) = sin 5x. Show that Y is a linearly independent subset of F. 7. Let X = {p1 , p2 , p3 }, where p1 (x) = x2 − 1, p2 (x) = x(x − 1), p3 (x) = x(x + 1). a) Show that X is a basis of P2 . b) Find the unique expression for the function defined by the formula p(x) = 9x2 − x − 4 as a linear combination of vectors in X ....
View Full Document

Ask a homework question - tutors are online