Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Textbook Question
Chapter 4.2, Problem 38EQ
Find the determinants in Exercises 35-40, assuming that
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Find the determinants in Exercises 35–40, assuming that
|a b c|
e f = 4
|g h i
|2a b/3 -c|
36. 2d e/3 -f|
-i|
|2a
2b 2c|
35. d
f
e
|2g h/3
|d
e f
- c bC
38. d -f e f
|g – i h i
37. a
b.
lg h
i
|2c b
39. 2f e
d
|2i h gl
a + 2g
b + 2h
c + 2i|
40. 3d + 2g 3e + 2h 3f + 2i
h
Find the determinants in Exercises 15-20, where
15.
a
b
d e f
3g 3h 3i
a
d
b с
e f = 7.
ghi
Prove using only the theorems of determinants:
b
-b -a
a
b
C
Id
-b -a
a
-d
C
C
d C
|=4(a² + b²)( c²+d²)
Chapter 4 Solutions
Linear Algebra: A Modern Introduction
Ch. 4.1 - In Exercises 1-6, show that is an eigenvector of A...Ch. 4.1 - In Exercises 1-6, show that vis an eigenvector of...Ch. 4.1 - Prob. 3EQCh. 4.1 - In Exercises 1-6, show that vis an eigenvector of...Ch. 4.1 - In Exercises 1-6, show that vis an eigenvector of...Ch. 4.1 - In Exercises 1-6, show that is an eigenvector of A...Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...
Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...Ch. 4.1 - In Exercises 7-12, show that is an eigenvector of...Ch. 4.1 - In Exercises 23-26, use the method of Example 4.5...Ch. 4.1 - In Exercises 23-26, use the method of Example 4.5...Ch. 4.1 - In Exercises 23-26, use the method of Example 4.5...Ch. 4.1 - In Exercises 31-34, find all of the eigenvalues of...Ch. 4.1 - Prob. 32EQCh. 4.1 - In Exercises 31-34, find all of the eigenvalues of...Ch. 4.1 - Consider again the matrix A in Exercise 35. Give...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 1-6 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Compute the determinants in Exercises 7-15 using...Ch. 4.2 - Prob. 24EQCh. 4.2 - Prob. 26EQCh. 4.2 - Prob. 27EQCh. 4.2 - In Exercises 26-34, use properties of determinants...Ch. 4.2 - Prob. 29EQCh. 4.2 - Prob. 30EQCh. 4.2 - Prob. 31EQCh. 4.2 - In Exercises 26-34, use properties of determinants...Ch. 4.2 - Prob. 33EQCh. 4.2 - In Exercises 26-34, use properties of determinants...Ch. 4.2 - Find the determinants in Exercises 35-40, assuming...Ch. 4.2 - Find the determinants in Exercises 35-40, assuming...Ch. 4.2 - Find the determinants in Exercises 35-40, assuming...Ch. 4.2 - Find the determinants in Exercises 35-40, assuming...Ch. 4.2 -
Find the determinants in Exercises 35-40,...Ch. 4.2 - Prob. 45EQCh. 4.2 - In Exercises 45 and 46, use Theorem 4.6 to find...Ch. 4.2 - In Exercises 47-52, assume that A and B are nn...Ch. 4.2 - In Exercises 47-52, assume that A and B are n n...Ch. 4.2 -
In Exercises 47-52, assume that A and B are n ×...Ch. 4.2 -
In Exercises 47-52, assume that A and B are n × n...Ch. 4.2 - In Exercises 47-52, assume that A and B are nn...Ch. 4.2 - In Exercises 47-52, assume that A and B are nn...Ch. 4.2 - Prob. 53EQCh. 4.2 - Prob. 57EQCh. 4.2 - Prob. 58EQCh. 4.2 - Prob. 59EQCh. 4.2 - In Exercises 57-60, use Cramer's Rule to solve the...Ch. 4.2 - Prob. 61EQCh. 4.2 - Prob. 62EQCh. 4.2 - Prob. 63EQCh. 4.2 - Prob. 64EQCh. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.3 - Prob. 2EQCh. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.3 - Prob. 7EQCh. 4.3 - In Exercises 1-12, compute (a) the characteristic...Ch. 4.4 - Prob. 5EQCh. 4.4 - Prob. 6EQCh. 4.4 - Prob. 7EQCh. 4.4 -
In general, it is difficult to show that two...Ch. 4.6 - Let x=x(t) be a twice-differentiable function and...
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- Find the determinants in Exercises 35-40, assuming that [abcdefghi]=4 [2ab/3c2de/3f2gh/3i]arrow_forwardFind the determinants in Exercises 35-40, assuming that [abcdefghi]=4 [2a2b2cdefghi]arrow_forwardCompute the determinants in Exercises 7-15 using cofactor expansion along any row or column that seems convenient. [0a0bcd0e0]arrow_forward
- Find the determinants in Exercises 35-40, assuming thatarrow_forwardCompute the determinants in Exercises 7-15 using cofactor expansion along any row or column that seems convenient. [000a00bc0defghij]arrow_forwardCompute the determinants in Exercises 7-15 using cofactor expansion along any row or column that seems convenient. 11.arrow_forward
- Verify an Equation In Exercises 63-68, evaluate the determinants to verify the equation. |wxyz|=|wx+cwyz+cy|arrow_forwardFill in the blanks with appropriate numbers to calculate the determinant. Where there is , choose the appropriate sign (+ or -).arrow_forwardCompute the determinants in Exercises 7-15 using cofactor expansion along any row or column that seems convenient. [522112300]arrow_forward
- Finding Determinants In Exercises 43-50, find (a)|AT|,(b)|A2|,(c)|AAT|,(d)|2A|, and (e)|A1|. A=[61145]arrow_forwardSolve using Cramer’s rule. 415. Evaluate the determinant by expanding by minors: |322214103|arrow_forwardFind a Determinant In Exercises 19-32, use expansion by cofactors to find the determinant of the matrix [xy1320111]arrow_forward
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