Unless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1-10 are invertible. Use as few calculations as possible. Justify your answers. 5 1. 3. 5. 7. 5 0 0 -3 -7 0 8 5 1 1 7 -4 03 3 ulo-5ot noijami 2 6. 7 9. [M] 0 -9 -1m-300 no 35 58 uqni-3 -2 -6 3 of 2 01-1m 201 Or -6 billo 2. 1 7 X-5 -5 -1 2 4. rollib 4b 0ing-7-7 11 10 3 L uloa botuamopga 9 19 -1 6-9 -7 0 3 0 1 0 8. Mo 0 0 20 adibat 1-5 0 -3 3 6 3 7 5 9 0 2 0 0 0 4 6 8 10
Unless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1-10 are invertible. Use as few calculations as possible. Justify your answers. 5 1. 3. 5. 7. 5 0 0 -3 -7 0 8 5 1 1 7 -4 03 3 ulo-5ot noijami 2 6. 7 9. [M] 0 -9 -1m-300 no 35 58 uqni-3 -2 -6 3 of 2 01-1m 201 Or -6 billo 2. 1 7 X-5 -5 -1 2 4. rollib 4b 0ing-7-7 11 10 3 L uloa botuamopga 9 19 -1 6-9 -7 0 3 0 1 0 8. Mo 0 0 20 adibat 1-5 0 -3 3 6 3 7 5 9 0 2 0 0 0 4 6 8 10
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
Related questions
Question
9
![h
S
r
m
py
nd
Unless otherwise specified, assume that all matrices in these
exercises are n xn. Determine which of the matrices in Exercises
1-10 are invertible. Use as few calculations as possible. Justify
your answers. molave ovios nodi bas.(E)
1.
3.
5.
7.
5
-3 -6
5
-3
8
0
1
-4
9. [M]
10. [M]
0
-7
b5
-1-3
3 00 5 8uq-3
-2
0
5679x
0
0
51
0
-9
odl bail,ban 2.
3o-5ot noijami
2
6.
7
-6
-6301 2
1
-1 201q98
4b
4.
Tollib
3
4
-4
tuloa batuqmona
-7 -7
1
11
9
7 X-5
10
19
-100 2 3 -1
Ooo 120 011
8.
6 -9
-7 0
3 0
5 3 10 dig 9
6 4% no-9 021-5
8 5 2
11 4
2 0
191
1 -5
0
3
-3
6
350
1 ob 217 ib vn97
2X81-8 gib
m
-1
7
4
0
96
0
28
0 0 0 10
9
-4
4
0
In Exercises 11 and 12, the matrices are all n x n. Each part of
the exercises is an implication of the form "If "statement 1",
then "statement 2"." Mark an implication as True if the truth of
"statement 2" always follows whenever "statement 1" happens
to be true. An implication is False if there is an instance in
which "statement 2" is false but "statement 1" is true. Justify each
answer.
a. If the equation Ax = 0 has only the trivial solution, then
A is row equivalent to the n x n identity matrix.
b. If the columns of A span R", then the columns are linearly
independent.
c. If A is an n x n matrix, then the equation Ax = b has at
least one solution for each b in R".
d. If the equation Ax=0 has a nontrivial solution, then A
d. If the linear transforma
then A has n pivot posi
e. If there is a b in R"
inconsistent, then the
to-one.
13. An mxn upper triang
below the main diagonal
is a square upper triangu
answer.
14. An mxn lower triang
above the main diagona
is a square lower triang
answer.
15. Can a square matrix wi
ible? Why or why not?
16. Is it possible for a 5 x
columns do not span R
17. If A is invertible, ther
independent. Explain w
18. If C is 6 x 6 and the
v in R6, is it possible t
has more than ore solu
19. If the columns of a 7 >
what can you say abou
20. If nxn matrices E an
then E and F commute
21. If the equation Gx =
y in R", can the colun
22. If the equation Hx =
can you say about the
23. If an n x n matrix K
you say about the col
24. If L is n x n and the e
do the columns of Ls
25. Verify the boxed stat
26. Explain why the co
columns of A are line
Show that if AB is inv
27](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8eddd3e4-97b2-4f20-b642-1ed0827b897f%2Ff175fa58-34c2-455e-8f22-554bf954d070%2Fl9uqw7w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:h
S
r
m
py
nd
Unless otherwise specified, assume that all matrices in these
exercises are n xn. Determine which of the matrices in Exercises
1-10 are invertible. Use as few calculations as possible. Justify
your answers. molave ovios nodi bas.(E)
1.
3.
5.
7.
5
-3 -6
5
-3
8
0
1
-4
9. [M]
10. [M]
0
-7
b5
-1-3
3 00 5 8uq-3
-2
0
5679x
0
0
51
0
-9
odl bail,ban 2.
3o-5ot noijami
2
6.
7
-6
-6301 2
1
-1 201q98
4b
4.
Tollib
3
4
-4
tuloa batuqmona
-7 -7
1
11
9
7 X-5
10
19
-100 2 3 -1
Ooo 120 011
8.
6 -9
-7 0
3 0
5 3 10 dig 9
6 4% no-9 021-5
8 5 2
11 4
2 0
191
1 -5
0
3
-3
6
350
1 ob 217 ib vn97
2X81-8 gib
m
-1
7
4
0
96
0
28
0 0 0 10
9
-4
4
0
In Exercises 11 and 12, the matrices are all n x n. Each part of
the exercises is an implication of the form "If "statement 1",
then "statement 2"." Mark an implication as True if the truth of
"statement 2" always follows whenever "statement 1" happens
to be true. An implication is False if there is an instance in
which "statement 2" is false but "statement 1" is true. Justify each
answer.
a. If the equation Ax = 0 has only the trivial solution, then
A is row equivalent to the n x n identity matrix.
b. If the columns of A span R", then the columns are linearly
independent.
c. If A is an n x n matrix, then the equation Ax = b has at
least one solution for each b in R".
d. If the equation Ax=0 has a nontrivial solution, then A
d. If the linear transforma
then A has n pivot posi
e. If there is a b in R"
inconsistent, then the
to-one.
13. An mxn upper triang
below the main diagonal
is a square upper triangu
answer.
14. An mxn lower triang
above the main diagona
is a square lower triang
answer.
15. Can a square matrix wi
ible? Why or why not?
16. Is it possible for a 5 x
columns do not span R
17. If A is invertible, ther
independent. Explain w
18. If C is 6 x 6 and the
v in R6, is it possible t
has more than ore solu
19. If the columns of a 7 >
what can you say abou
20. If nxn matrices E an
then E and F commute
21. If the equation Gx =
y in R", can the colun
22. If the equation Hx =
can you say about the
23. If an n x n matrix K
you say about the col
24. If L is n x n and the e
do the columns of Ls
25. Verify the boxed stat
26. Explain why the co
columns of A are line
Show that if AB is inv
27
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