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Matrix Unit Test
Contributed by: Cox
2     -2     3
1     -2      0
9      7     -1
1.  Find the determinant of     the matrix.
2.  Use Cramer's Rule to solve.
-5x + 7y = -38
-8x - 6y = 8
3.  Find the inverse, if it exists.
R1C1:
R2C1:
A =
5         8
4         9
R1C2:
R2C2:
4.  Solve for Y:  
Y + 
R1C1:
R2C1:
-11  -10
9     -11
=
R1C2:
R2C2:
-3      -13
-5         1
R1C1:
R3C1:
R2C1:
Find the products of AB, if possible.
A = 
-2       0
5       8
2       5
Is it possible?  Y/N   
R1C2:
R2C2:
R3C2:
B = 
7     0     -2
2     6       4
R1C3:
R2C3:
R3C3:
6.  Write the matrix equation for the system
     and solve.
7x - y = 4

-6x + y = -1
7.  Find the answer matrix.
R1C1:
R2C1:
9    -7
5    -5
-4   -1
7      1
R1C2:
R2C2:
8.  Solve for x, y, and z.
y+z      y        4
11    x+z     25
x = 
y = 
z = 
=
x-y     -5    25
-16    -20    z
9.  Find the determinant of the matrix.
5     -4    4
10    9    -1
1     -2    0
10.  Use Cramer's Rule to Solve.
-x -5y = 0

-4x - 8y = 12
11.  Write the matrix equation for the system
and solve.  
-7x + y = -10

-6x + y = 5
12.  Solve for matrix X.
-3     5
-6    -3
R2C1:
R1C1:
X = 
12    36
32   -8
R1C2:
R2C2:
13.  Find the Inverse of A, if it exists.
R1C1:
R2C1:
A-1 does not exist.  T/F  
A = 
-2    -1
2       6
R1C2:
R2C2:
14.  Solve for a, b, c, and d.
-16        b
a+c      -11
a = 
b = 
=
2+a       6
-38        d
c = 
d = 
15.  Find the product of BA, if it exists.
A = 
Does BA exist?  Y/N
If so, what is the product?
-4
4
6
B = 
-5   5   2 
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