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anonymous
 one year ago
Please explain how to find basis for set of 2x3 matrices whose null space contains (2, 1, 1). This is a question from Recitation video in
http://ocw.mit.edu/courses/mathematics/1806sclinearalgebrafall2011/axbandthefoursubspaces/matrixspacesrank1smallworldgraphs/
It's not very well explained in the video.
anonymous
 one year ago
Please explain how to find basis for set of 2x3 matrices whose null space contains (2, 1, 1). This is a question from Recitation video in http://ocw.mit.edu/courses/mathematics/1806sclinearalgebrafall2011/axbandthefoursubspaces/matrixspacesrank1smallworldgraphs/ It's not very well explained in the video.

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JoshDanziger23
 one year ago
Best ResponseYou've already chosen the best response.1Lokeshh, if A is a (2,3) matrix with u=(2,1,1) in its null space then it must be that both rows of A are orthogonal to u. Any two independent vectors v and w orthogonal to u will span a plane perpendicular to u, and the recitation lecturer suggests the two vectors v=(1,0,2) and w=(0,1,1) are natural choices. As long as the rows of A are linear combinations of v and w then we will have Au=0; and because v and w span the whole plane, linear combinations of v and w will generate all vectors orthogonal to u. So we can make a basis for all (2,3) matrices satisfying Au=0 by using the basis [1,0,2; 0,0,0], [0,1,1; 0,0,0], [0,0,0; 1,0,2], [0,0,0; 0,1,1]. Does that help? Josh.
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