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Math 203 Spring Z}1-l-Exarn 2
Instructor: Shaoiro
Work careftrlly and neatly and remember that I cannot gracle what I cannot read. You
must show all relevant work in the appropriate space. You rnay receive 1o credit for a correct
allswer if there is insufficient supporting lvork. Notes, books ancl graphing or prograrnable
ci-ilculators are NOT ALLOWED.
[21prtl 1. Fill in the blanks with,4 (Iways), S(ometi'mes). N(e,uer)so that the followirlg ar.e correct
stal,eurents.
(a) If A is a 3 x 5 matrix, then the columns of A u.. A linearly dependent.
(b) If A is a3 x 2 matrix, then the transformationxp+,4x is S one-to-one.
(c) If the rnatrix B is obtained frorn A by adding three times the first row to the third
t'ow of A. then lAl 5/ t', equals 3lBl.
(d) If A is invet'tible n x n matrix, then the matrix equation Ax : b, rvhere b is any
ru-tr.rple, A has a unique solutiou.
(e) If ,4 is a non-invertible square matrix, then the columns of A are A linearly
independent.
(f) If A is a 5 x 5 invertible rnatrix, then lAl S equals 2b.
(g) If ,4 is a scluare invertible matrix and B is obtained from ,4 by perforrning a sequelce
of stanclard elementary row operations on ,4, theu B is A invertible.
u) lA-'l b) l3Al c) 2a 2b 2c
3a*d 3b*e 3c+ f
shi
= j1 'f r ).{= ?
[15pt] 2. Let o:f i 2 ;land lAl : 4. compute the following determinants:
lg h i)
b-!
.?
