Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Chapter 4.4, Problem 41EQ
In general, it is difficult to show that two matrices are similar. However, if two similar matrices are diagonalizable, the task becomes easier. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. Then find an invertible matrix P such that
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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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- Name: Tay Jones Level Two Date: Algebra 3 Unit 3: Functions and Equations Practice Assessment Class: #7-OneNote 1. The function f(x) = x² is transformed in the following functions. List the vertex for each function, circle whether the function opens up or down, and why. All three parts must be correct to receive Level 2 points. You can receive points for a, b, and c. a) g(x) = -2(x+5)² Vertex: Opens Up Opens Down Why? ais negative -2 Vertex: b) g(x) = (x + 2)² - 3 c) g(x) = -4(x + 2)² + 2 Opens Up Opens Down Vertex: Opens Up Opens Down Why? 4 Ca is negative) Why? his positive 2. The graph of the function f(x) is shown below. Find the domain, range, and end behavior. Then list the values of x for which the function values are increasing and decreasing. f(x) Domain: End Behavior: As x → ∞o, f(x) -> -6 As x, f(x) -> Range: Where is it Increasing? (002] Where is it Decreasing? (1,00)arrow_forwardShow what to do on the graph visually please!arrow_forwardThe county's new asphalt paving machine can surface 1 km of highway in 10 h. A much older machine can surface 1 km in 18 h. How long will it take them to surface 21 km of highway if they start at opposite ends and work day and night?arrow_forward
- 3. Write a system of linear equations in slope intercept form that has exactly one solution at the point (3, 4), such that one line has positive slope (but not 1) and the other line has negative slope (but not "1). Also write your system of equations with both equations written in standard form with out any fractions 8- 7 8 5 4 3 -2- + -8-7-6-5-4-3-2-1 1 2 3 -1 2 - ° 4 -5 - -8arrow_forward2. Write a system of linear equations in slope-intercept form has exactly one solution at the point (3, 4), such that both lines have negative slope (but neither one has slope of 1). Also write your system of equations with both equations written in standard form without any fractions. B 0 5 4 3 -2 1 -8-7-6-5-4-3-2 -1 12 3 -1 2 -3 -5 6 -7 -8arrow_forward4. Write a system of linear equations in slope-intercept form that has no solution, such that (3, 4), and (3,8) are solutions to the first equation, and (0, 4) is a solution to the second equation. Also write your system of equations with both equations written in standard form with out any fractions B 0 5 4 3 -2 + -8-7-6-5-4-3-2 -1 |- 1 2 3 -1 2 -3 4 -5 6 -7arrow_forward
- Show how you can solve the system of equations by manipulating the algebra tiles while maintaining the balances. On this side of the page, use the addition (elimination) method. Keep track of what you did at each step by writing down the corresponding equivalent equations, as well as what you did to go from one equation to the next. 1. x + 2y = 5 x-2y=1 2. 2x+y=2 x-2y= 6arrow_forwarde) x24 1) Which of these are equivalent to x³? For each expression that is equivalent to x², prove it by using the definition of exponents. For each that is not equivalent to x³, give an example using a specific value for x that shows that it represents a different number. a) (x5) d) f) 10-2 b) (x²) *|*arrow_forwardNow show how you can solve the system of equations by manipulating the algebra tiles while maintaining the balances, using the substitution method. Keep track of what you did at each step by writing down the corresponding equivalent equations, as well as what you did to go from one equation to the next. Δ 1. x + 2y = 5 x-2y=1 2. 2x + y = 2 x-2y= 6arrow_forward
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