Test the set S= {w, x, y, z) of the following 4 vectors to identify a...

Transcribed Image Text:

Test the set S= {w, x, y, z) of the following 4 vectors to identify a subset U containing the maximum number of linearly independent ones. Express then the linearly dependent ones in the form of linear combination of the vectors in U. w, x, y, z = (1, 2, 2), (0, 1, 4), (2, 3, 0), (3, 0,-1); W, x, y, z := 2 O 2 3 (4.1) (B) Does the set U span the Euclidean space R³? If it does express an arbitrary vector b in that space, b = (b1,b2, b3) = R³, as a linear combination of the vectors you included in U. Check that your linear combination is correct. Test the set S= {w, x, y, z) of the following 4 vectors to identify a subset U containing the maximum number of linearly independent ones. Express then the linearly dependent ones in the form of linear combination of the vectors in U. w, x, y, z = (1, 2, 2), (0, 1, 4), (2, 3, 0), (3, 0,-1); W, x, y, z := 2 O 2 3 (4.1) (B) Does the set U span the Euclidean space R³? If it does express an arbitrary vector b in that space, b = (b1,b2, b3) = R³, as a linear combination of the vectors you included in U. Check that your linear combination is correct.

Answer rating: 100% (QA)

A First we need to compute the determinant of the matrix formed by the set Swxyz 1 2 2 0 1 4 2 3 0 3 ... View the full answer