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Unformatted text preview: MATH 20F PRACTICE FINAL - 28 JULY, 2OO8 Name: (1) True or False? Circle one. T F (a) The row space of A is the column space of A T T F (b) The inverse of an invertible n n matrix A can be found by row reducing the augmented matrix [ A | I n ]. T F (c) If B and C are two bases for a finite dimensional vector space V then B and C have the same number of vectors in them. T F (d) Two vectors ~u and ~v in R n are orthogonal if and only if their dot product, ~u ~v , is greater than or equal to ~ 0. T F (e) If B is a basis for a finite dimensional vector space V and C is a basis for a subspace of V then each vector in C can be written as a linear combination of the vectors in B . T F (f) The area of the parallelogram whose corners have coordinates (0 , 0) , (1 , 0) , (2 , 3) , and (3 , 3) is 9. T F (g) If m < n then the columns of an m n matrix A could span R n . T F (h) If A and B are row equivalent matrices then Row( A ) = Row( B ). T F (i) If the second column in a matrix is a pivot column then x 2 is not a free variable....
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