Homework 4A
Name___________________________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1) Find the result of performing the elementary row operation R 3 + (5) R 2 on the system
1 0 3 9
0 1 -3 2 .
0 -5 4 1 1) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1
2) The system 0
1
A)
1 0 0
0 1 -3
0 1 -3 0 0 -2
1 3 5 is equivalent to the system
1 -3 4
B)
C)
-2
1 0 0 -2
1 0 0 -2
.
.
5
0 1 -3 5
0 1 3 5 .
4
0 0 0 4
0 1 -3 6 2)
D)
1 0 0 -2
0 3 -9 5 .
1 1 -3 4 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use the indicated row operation to change the matrix.
3) Replace R 2 by 1 R 1 + 1 R 2.
3
2 3) 3 0 12
-2 4 6
Use the Gauss-Jordan method to solve the system of equations.
4)
3x + 5y = 16
3x = -9
5) 4) 5)
x - y + 4z = -6
5x + z = -1
x + 3y + z = 5 6) Pivot the matrix 1 3 about the element 3.
4 -2 6) Solve the system of linear equations using the Gaussian elimination method. If there is no solution, state so; if there
are infinitely many solutions, find two of them.
7)
7)
x - y + 2z = 2
y - 2z = 1
-3x + 5y - 10z = -4 1 8) 8)
x - y - 2z = 2
y - 2z = 1
-3x + 5y - 10z = -4 For the system of equations, state whether there is one, none, or infinitely many solutions. If there are one or more
solutions, give all values of x, y, and z that satisfy the system.
9)
9)
x+y- z = 1
y - 2z = 1
x+y- z = 2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
x - y = 7 . Which of the following statements is true?
2x - 2y = k
A) If k = 10, the system has infinitely many solutions.
B) If k = 10, the system has no solution.
C) If k ≠ 10, the system has exactly one solution.
D) none of these 10) Consider the system: 10) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use the Gauss-Jordan method to solve the system of equations.
11) -4x - 2y = 6
-16x - 8y = -1 11) Perform the matrix operation.
12) Let A = 1 3 and B = 0 4
2 6
-1 6 . Find 4A + B. 12) . Find C - 4D. 13) 1
13) Let C = -3
2 and D = -1
3
-2 Find the matrix product AB, if it is defined.
14) A = -1 3 , B = -2 0 .
2 2
-1 4 15) A = 3 -2 1
0 4 -2
16) A = 1 3 -2
2 0 3 , B= 4 0
-2 3 3 0
, B = -2 1
0 3 14) . 15) . 16) 2 17) Write the system of linear equations as a matrix equation.
x + 2y + 3z = 4
6y + 7z = 8
x
= 5
Write the matrix equation as a system of linear equations without matrices.
18)
-7 0
-8
x1
=
1 1
8
x2
-8 -5
-7 3 17) 18)

 

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