Unformatted text preview: U 1 + W = U 2 + W , then U 1 = U 2 . Problem 5: Subspaces. Consider the space F oF all Functions f : R + → R , which have a Laplace transForm ˆ f ( s ) = i ∞ f ( t ) est dt defned For all Re ( s ) > 0. ²or some fxed s in the right halF plane, is { f  ˆ f ( s ) = 0 } a subspace oF F ? Problem 6: Linear Independence. Which oF the Following sets are linearly independent in R 3 ? 1 2 , 2 1 , 5 1 , 4 5 1 , 1 21 , 2 1 3 Problem 7: Bases. Let U be the subspace oF R 5 defned by U = { [ x 1 ,x 2 ,...,x 5 ] T ∈ R 5 : x 1 = 3 x 2 and x 3 = 7 x 4 } ²ind a basis For U . Problem 8: Bases. Prove that iF { v 1 ,v 2 ,...v n } is linearly independent in V , then so is the set { v 1v 2 ,v 2v 3 ,...,v n1v n ,v n } . 1...
View
Full Document
 Fall '10
 ClaireTomlin
 Electrical Engineering, Linear Algebra, Vector Space, um ∈ Um

Click to edit the document details