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Unformatted text preview: i.e., A = 0. C
is true by a theorem and for A you can easily ﬁnd counterexamples, for instance A =
diag( − 1, 1, 1, 1, , 1).
3. (2). C is not given by a homegenous linear condition, A and B are.
4. (2). The two equations are clearly independent, so the dimension is 4 − 2 = 2.
5. (4). The second column of A is − 2 times the ﬁrst, so it is unnecessary. Perform GramSchmidt on the other two.
6. (3). W = span{[1, 0, 0], [0, 1, 1]} and that basis is orthogonal, so the required distance is
√
the norm of X − projWX = X − 3[1, 0, 0] −...
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This note was uploaded on 01/19/2010 for the course MAT MAT223 taught by Professor Uppal during the Spring '09 term at University of Toronto Toronto.
 Spring '09
 UPPAL
 Linear Algebra, Algebra, Vectors

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