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 nonzero 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.
 Fall '05
 HUI
 Linear Algebra, Algebra, Vectors

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