Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Find a basis and the dimension for each of the following subspace W :
W = span{(1, 1, −1), (3, 5, −1), (1, 2, 0), (−1, 1, 3)}.
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- doing rref I believe dimension is 3, but I'm not sure how to state the basis or how to find the orthogonal basisarrow_forwardFind a basis for the orthogonal complement of the subspace of Rª spanned by the following vectors. V1 = (1,-1,7,3), V2 = (2,-1,5,2), V3 = (1, 0, -2, -1) The required basis can be written in the form {(x, y, 1, 0), (z, w, 0, 1)}.arrow_forwardFor the subspace below, (a) find a basis, and (b) state the dimension. 6a + 12b 2c 9a - 3b - 3c - 12a + 5b + 4c - - 3a + b + c : a, b, c in R a. Find a basis for the subspace. A basis for the subspace is . (Use a comma to separate vectors as needed.) b. State the dimension. The dimension is 2.arrow_forward
- helparrow_forwardPlease provide detailsarrow_forwardSuppose a subspace is spanned by the set S of vectors shown. Find a subset of S that forms a basis for the subspace, using the method of transforming a matrix to echelon form, where the columns of the matrix represent vectors spanning the subspace. GOL S= A basis is -3 16 20 What is the dimension of the subspace?arrow_forward
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