of determi- 13. 5 4 76 6-2-4 2 4 1 2 0 7 7 0 14. 1 5 0-2 3 5 4 5 5 4 -4 0 1 0 -6 Wab Find the determinants in Exercises 15-20, where Inima b c -6 180
of determi- 13. 5 4 76 6-2-4 2 4 1 2 0 7 7 0 14. 1 5 0-2 3 5 4 5 5 4 -4 0 1 0 -6 Wab Find the determinants in Exercises 15-20, where Inima b c -6 180
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
13
![9.
1.
11.
1
2. 0
3
3
3. 3
1
7.
3.2 EXERCISES
nants. State the property.
Each equation in Exercises 1-4 illustrates a property of determi-
]
01-
1
4. 2
0
1 -3
4
-1
* * * *
3 -5
5 -2
6
8
-2
-6
5. -1 -4
-2 -8
1
10210
3
3
-6
6
1st or 2400
2
3 -4 =
7
5 -5
3
1 3
244
2
3 -4
0 -3
1 5 -4
5
7
3 5
-1
953
-1 0
†♡~
0
-5 7
=
||
3 -1
= 33
WWAO WAN
1 -1 -3 0
0 1
when ther
5
3 -3 -2
Find the determinants in Exercises 5-10 by row reduction to
echelon form.
(360110
2
2
2 -3
4
5 4
6232
10. -2 -6 2
5 -6
2 -4 5
2 -4 -2
1 -3
0
4 −1
13
3
4 -3 -1
01-3
0-4
8 -4
1
2
0 3 -4
0
-2
1 3 -4
0-6 5
3 -5 2
-wn Iaw
-2
5-2
-2
0
8.
-6
1 3 3
10
-3
9
súre
5 -5
3
629
bm 3 3 -3
6. 3 4 -4
2 -3 -5
CARUSO
12.
8
1023
2. Use a determinant to decide if V₁, V2, and v3 are linearly independent, when
2
V3 = -7
--[1]
5
3
11
4
-3 -10 -7 2
Combine the methods of row reduction and cofactor expansion to
compute the determinants in Exercises 11-14.
3 2-4
1 2 -5
7 6 -3
5
-[-]
I.
3. Let A be an n x n matrix such that A² = 1. Show that det A = ±1. marz
V₁ =
2 3 0
4
4
2 4 3
30
66
ALA
13.
15.
17.
21.
25.
V2 =
a
d
3g
24.
2
4
4
6
6-2 -4
-6
7 7
5727
(
a
19. 2d + a
g
25.
a
20. d + 3g
8
8 Job
Find the determinants in Exercises 15-20, where
b
a + d
d
g
3.2 Properties of Determinants 177
-3
3
[]
-5
b
e
3h
a
d
g
4
b + e
e
h
1200
C
f
AX ai
3i
b
2e + b
h
2 6 0
1
312
39 2
2 0
1 -7 -5
3 8
0
7
14.
on
hi
i
6
0
6
0
5 4
-6
C
f = 7.
det
c + f
f
i
1 5 4
-4
0-2
3
5
6
0
-5
800
C
2f + c
i ob
S5
18.
In Exercises 21-23, use determinants to find out if the matrix is
invertible.
-8
-4
5
BOD
7
5
a
16. 5d
g
0
b
C
e + 3h f + 3i
h tob mad ildi ovni ai A ti sart
Isups od 22.
d
connam
4
5
a
8
1
0
1
1
0
b
bo
с
5em 5f
h
i
e
f
bc
h
i
12=0isb
In Exercises 24-26, use determinants to decide if the set of vectors
is linearly independent.
noirmskaxs
1 -1]
مریکا در
5
1 -3 -2
0
5
wit](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe5db299-428d-40d7-abe3-e166485c95d7%2F6f3c3e84-89b8-4242-af85-16badab463eb%2F1j934i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:9.
1.
11.
1
2. 0
3
3
3. 3
1
7.
3.2 EXERCISES
nants. State the property.
Each equation in Exercises 1-4 illustrates a property of determi-
]
01-
1
4. 2
0
1 -3
4
-1
* * * *
3 -5
5 -2
6
8
-2
-6
5. -1 -4
-2 -8
1
10210
3
3
-6
6
1st or 2400
2
3 -4 =
7
5 -5
3
1 3
244
2
3 -4
0 -3
1 5 -4
5
7
3 5
-1
953
-1 0
†♡~
0
-5 7
=
||
3 -1
= 33
WWAO WAN
1 -1 -3 0
0 1
when ther
5
3 -3 -2
Find the determinants in Exercises 5-10 by row reduction to
echelon form.
(360110
2
2
2 -3
4
5 4
6232
10. -2 -6 2
5 -6
2 -4 5
2 -4 -2
1 -3
0
4 −1
13
3
4 -3 -1
01-3
0-4
8 -4
1
2
0 3 -4
0
-2
1 3 -4
0-6 5
3 -5 2
-wn Iaw
-2
5-2
-2
0
8.
-6
1 3 3
10
-3
9
súre
5 -5
3
629
bm 3 3 -3
6. 3 4 -4
2 -3 -5
CARUSO
12.
8
1023
2. Use a determinant to decide if V₁, V2, and v3 are linearly independent, when
2
V3 = -7
--[1]
5
3
11
4
-3 -10 -7 2
Combine the methods of row reduction and cofactor expansion to
compute the determinants in Exercises 11-14.
3 2-4
1 2 -5
7 6 -3
5
-[-]
I.
3. Let A be an n x n matrix such that A² = 1. Show that det A = ±1. marz
V₁ =
2 3 0
4
4
2 4 3
30
66
ALA
13.
15.
17.
21.
25.
V2 =
a
d
3g
24.
2
4
4
6
6-2 -4
-6
7 7
5727
(
a
19. 2d + a
g
25.
a
20. d + 3g
8
8 Job
Find the determinants in Exercises 15-20, where
b
a + d
d
g
3.2 Properties of Determinants 177
-3
3
[]
-5
b
e
3h
a
d
g
4
b + e
e
h
1200
C
f
AX ai
3i
b
2e + b
h
2 6 0
1
312
39 2
2 0
1 -7 -5
3 8
0
7
14.
on
hi
i
6
0
6
0
5 4
-6
C
f = 7.
det
c + f
f
i
1 5 4
-4
0-2
3
5
6
0
-5
800
C
2f + c
i ob
S5
18.
In Exercises 21-23, use determinants to find out if the matrix is
invertible.
-8
-4
5
BOD
7
5
a
16. 5d
g
0
b
C
e + 3h f + 3i
h tob mad ildi ovni ai A ti sart
Isups od 22.
d
connam
4
5
a
8
1
0
1
1
0
b
bo
с
5em 5f
h
i
e
f
bc
h
i
12=0isb
In Exercises 24-26, use determinants to decide if the set of vectors
is linearly independent.
noirmskaxs
1 -1]
مریکا در
5
1 -3 -2
0
5
wit
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education