Prelim 2 [Solutions]

A 30 3 points for any 2 3 matrix a the null space of

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Unformatted text preview: 3 points, leaving a question blank is worth 0 points, and an incorrect answer is worth −3 points. a) (3/0/ − 3 points) For any 2 × 3 matrix A, the null space of A is perpendicular to the null space of AT . b) (3/0/ − 3 points) Let ￿1 , ￿2 , ￿3 be non-zero vectors in R3 . If every pair of ￿1 , ￿2 and ￿3 vvv vv v 3 are perpendicular, then {￿1 , ￿2 , ￿3 } is a basis of R . vvv c) (3/0/ − 3 points) Every (positive dimensional) subspace S of Rn has an orthonormal basis. d) (3/0/ − 3 points) If ￿ and ￿ are 3 × 1, then ￿ ￿ T has determinant 0. u v uv Solution: (a) F...
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This note was uploaded on 01/30/2014 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell.

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