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Math 1090
Final, Page 4 of 13
27 April, 2012
3. (15 points) Given the following matrices, perform the indicated operations. If not possible, state the reason why.


�
�
�
�
1 3
4 1
5 9
A=
B=
C = 3 4
3 2
0 7
5 6
(a) Give the size of each matrix.
(b) Calculate A + B T
(c) Calculate C · A
(d) Calculate A · C
Math 1090
Final, Page 5 of 13
27 April, 2012
4. (15 points) (a) Find the inverse of
�
4 −3
A=
−5 4
�
(b) Solve the following system of equations:
4x − 3y = 23
−5x + 4y = 10
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4x + 7
2(# y =
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4
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y=
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#
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#2x + 6z = 6
%
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%
& "y " 3z = "7
#
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70/83.6#>>9#:+4;.0<#======================================#
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(8 pts) 4. Solve the following linear system. Write your answers as an
ordered triple.
# x + 2y + 3z = "3
%
$ "2x + y " z = 6
%
& 3x " 3y + 2z = "11
!
Answer 4:______________________________
# 2x " y = 4
%
(6 pts) 2. $ 3x " 7y + 2z = "5
%
& 7y " 4z = 0
a) Write the augmented matrix that corresponds to this system of linear equations.
b) Write the matrix equation that corresponds to this system of linear equations.
!
!
!
(10 pts) 1. Find the inverse of the matrix A.
"1 1 0 %
'
$
A = $6 2 3'
$#1 0 1 '&
!
A-1 =_________________________
5. For
5x + 6y = 4
2x + 3y = 1
(a) (8 Points) Rewrite this system of linear equations Matrix form (i.e A ( xy ) = B,
where A is a matrix and B is a vector).
A=
B=
(b) (6 Points) Find A−1 .
A−1 =
(c) (6 Points) Solve for x and y.
(x, y) =
8
3. [14 points] (a) Given the matrix A =
method.
�
4 6
5 7
�
find its inverse. You may use any
(a)
(b) Given the system of equations:
�
3x + y = 1
4x + 2y = 2
Write this system in matrix form. i.e. Write it in the form A�x = �b where A is a
matrix and �x and �b are vectors.
(b)
(c) For A =
�
1 3 7
2 4 0
�

−2 1
and B =  5 −1 , find 2A + B T .
3
9

(c)
1. Solve the following linear system of equations using an augmented matrix. Be sure
to clearly indicate each step of your solution.
# x + y " z = "3
%
$ 4 x + 2z = 8
%
& x " 2y + z = 7
!