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Chapter 8 Pre Test


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Write the system of linear equations represented by the augmented matrix. (Use variables x, y, z, and w.)
mc001-1.jpg
a.
mc001-2.jpg
b.
mc001-3.jpg
c.
mc001-4.jpg
d.
mc001-5.jpg
e.
mc001-6.jpg
 

 2. 
Identify the elementary row operation being performed to obtain the new row-equivalent matrix.
Original Matrix
New Row-Equivalent Matrix
mc002-1.jpg
mc002-2.jpg
a.
Add –2 times R2 to R1.
b.
Add 2 times R2 to R1.
c.
Add –2 times R1 to R2.
d.
Add 2 times R1 to R2.
e.
Add 2 times R1 to R1.
 

 3. 
Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.)
mc003-1.jpg
a.
x = 83, y = –5, z = –4
b.
x = –2, y = –1, z = 3
c.
x = –1, y = 2, z = –3
d.
x = –1, y = –2, z = 3
e.
x = 2, y = 3, z = 1
 

 4. 
Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.
mc004-1.jpg
mc004-2.jpg
a.
The systems yield different solutions.
b.
x = 3, y = 6, z = 2
c.
x = –6, y = 2, z = –3
d.
x = –3, y = –6, z = 2
e.
x = 3, y = 2, z = –3
 

 5. 
The currents in an electrical network are given by the solutions of the system
mc005-1.jpg
where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.
a.
I1 = 3, I2 = 5, I3 = 8
b.
I1 = 5, I2 = 3, I3 = 8
c.
no solution
d.
I1 = 5, I2 = 8, I3 = 3
e.
I1 = 3, I2 = 5, I3 = 9
 

 6. 
Evaluate the expression.
mc006-1.jpg
a.
not possible
b.
mc006-2.jpg
c.
mc006-3.jpg
d.
mc006-4.jpg
e.
mc006-5.jpg
 

 7. 
Evaluate the expression.
mc007-1.jpg
a.
mc007-2.jpg
b.
not possible
c.
mc007-3.jpg
d.
mc007-4.jpg
e.
mc007-5.jpg
 

 8. 
If possible, find AB.
mc008-1.jpg
a.
mc008-2.jpg
b.
not possible
c.
mc008-3.jpg
d.
mc008-4.jpg
e.
mc008-5.jpg
 

 9. 
Use the matrix capabilities of a graphing utility to find AB, if possible.
mc009-1.jpg
a.
not possible
b.
mc009-2.jpg
c.
mc009-3.jpg
d.
mc009-4.jpg
e.
mc009-5.jpg
 

 10. 
Find the inverse of the matrix mc010-1.jpg.
a.
mc010-2.jpg
b.
mc010-3.jpg
c.
mc010-4.jpg
d.
mc010-5.jpg
e.
mc010-6.jpg
 

 11. 
Find the inverse of the matrix mc011-1.jpg (if it exists).
a.
mc011-2.jpg
b.
mc011-3.jpg
c.
mc011-4.jpg
d.
mc011-5.jpg
e.
does not exist
 

 12. 
Solve the system of linear equations
mc012-1.jpg
using the inverse matrix mc012-2.jpg.
a.
mc012-3.jpg
b.
mc012-4.jpg
c.
mc012-5.jpg
d.
mc012-6.jpg
e.
mc012-7.jpg
 

 13. 
Solve the system of linear equations
mc013-1.jpg
using the inverse matrix mc013-2.jpg.
a.
mc013-3.jpg
d.
mc013-6.jpg
b.
mc013-4.jpg
e.
mc013-7.jpg
c.
mc013-5.jpg
 

 14. 
Solve the system of linear equations
mc014-1.jpg using an inverse matrix.
a.
mc014-2.jpg
b.
mc014-3.jpg
c.
mc014-4.jpg
d.
mc014-5.jpg
e.
mc014-6.jpg
 

 15. 
Find the determinant of mc015-1.jpg.
a.
7
b.
–4
c.
mc015-2.jpg
d.
8
e.
–3
 

 16. 
Use the matrix capabilities of a graphing utility to find the determinant of the matrix
mc016-1.jpg.
a.
4
b.
–12
c.
7
d.
–10
e.
–6
 

 17. 
Use the matrix capabilities of a graphing utility to find the determinant of the matrix
mc017-1.jpg.
a.
–384
b.
–32
c.
–64
d.
–48
e.
128
 

 18. 
Givenmc018-1.jpg, find mc018-2.jpg.
a.
88
b.
–120
c.
168
d.
40
e.
–80
 

 19. 
Solve for x given the following equation involving a determinant.
mc019-1.jpg
a.
mc019-2.jpg
b.
mc019-3.jpg
c.
mc019-4.jpg
d.
mc019-5.jpg
e.
mc019-6.jpg
 

 20. 
Use a determinant to find y such that mc020-1.jpg, and mc020-2.jpg are collinear.
a.
mc020-3.jpg
b.
mc020-4.jpg
c.
mc020-5.jpg
d.
mc020-6.jpg
e.
mc020-7.jpg
 



 
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