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Unformatted text preview: Math 54 Midterm 1 Review Mike Hartglass September 26, 2010 1.) Let A denote the matrix A = 1 2 3 2 1 1 2 3 2 1 1 1 Find bases for the following spaces: Col( A ), Col( A 2 ), Nul( A ), Nul( A 2 ). 2.) Determine if the following statements are true or false: a. ) If A and B are invertible n × n matrices then so is A + B . b. ) If AB is invertible then A and B are invertible. c. ) If AB is invertible and A and B are n × n matrices then A and B are both invertible. d. ) If S is a linearly dependent set in some vector space V then S spans V . e. ) If T : R n → R m is a linear transformation and if { v 1 ,...,v n } is a basis for R n then { T ( v 1 ) ,...,T ( v n ) } is a basis for R m . f. ) Let T : V → W is a onetoone and onto linear transformation between vector spaces V and W . If { v 1 ,...,v n } is a basis for V then { T ( v 1 ) ,...,T ( v n ) } is a basis for W ....
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This note was uploaded on 11/19/2010 for the course LECTURE 1 taught by Professor Yildiz during the Fall '10 term at Berkeley.
 Fall '10
 yildiz
 Math

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