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Unformatted text preview: September 17, 2009 Math. 225  Quiz 3 Use both sides of the paper if necessary
(1) Let A = 3
1 2 0
.
and b =
8
−2 3 7 (a) Rewrite the matrix equation AX = b as a vector equation. [Hint:
use the columns of A]. 1
3
(b) Given that X = 1 and X ′ = 0 are both solutions to the AX = b,
1
2
without doing any row reduction or elimination, write down a solution to the
homogeneous equation AX = 0. 2
3 0 , and C = 2.
(2) Let A = 1 2 −1 , B =
−3
3 (a) compute both AB and BA.
(b) Compute, or say why it can’t be done: A + B, A + C, B + C Solutions
(1a)
x1 1
2
0
3
+ x2
+ x3
=
−2
3
7
8 (1b) If X and X ′ are solutions to Ax = b then A(X − X ′ ) = 0, i.e. the
solution asked for is −2
X − X′ = 0 −1 (2a)
AB = 2 + 0 + 3 = 5 , 2
4 −1
0
0
BA = 0
−3 −6 3 (2b) Addition is deﬁned only for matrices of the same shape. Since A is a
3 × 1 matrix but B and C are 1 × 3 matrices it follows that only B + C is
deﬁned. 2+3
5 0 + 2 = 2
B+C =
−3 + 3
0 ...
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This note was uploaded on 09/01/2010 for the course MATH math 225 taught by Professor Bradlow during the Fall '09 term at University of Illinois at Urbana–Champaign.
 Fall '09
 bradlow
 Math

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