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Unformatted text preview: englishMATlI 33A LECTURE 1 1ST MIDTERM 2 Problem 1. (True / False, 2 pts each) Mark your answers by ﬁlling in the appropriate box
next to each question. The matrix 001—1 1
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x wowo :3 There are no two 2 matrices A and B for which AB = BA. 1 7 6
i If the matrix of a linear transformation T is 14 20 3 ] , then
11 22 9 21m: (iv: IE) There is a 3 x 4 matrix A with kerA = {0}.
" I) A 3 x 3 invertible matrix always has rank 3.
If A is an invertible 3 x 3 matrix, then the image of A is spanned by the vectors (v1
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0 , 1 , 0
0 O 1
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7009 456 ,englishMATH 33AMLECTURE 1 Find a basis % for the image and %’ for the kernel of A. (b) Let 12
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me (where Q3 is your basis for the image from part (a)). Problem 2. (20 pts) (a) Let g
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Compute {H2007 and [TF7 (Hint: 27 is odd). AWN
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Show that ker AB = ker B. (b) Express the rank of AB in terms of the rank of B. f“ a 3: 3‘ ﬂ 3 E W,“ fl“, m r
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