College Algebra (10th Edition)
10th Edition
ISBN: 9780321979476
Author: Michael Sullivan
Publisher: PEARSON
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Textbook Question
Chapter 9.1, Problem 83AE
Car Loans Phil bought a car by taking out a loan for at interest per month. Phil's normal monthly payment is per month, but he decides that he can afford to pay extra toward the balance each month. His balance each month is given by the recursively defined sequence
Determine Phil’s balance after making the first payment. That is, determine .
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Question 3
over a field K.
In this question, MË(K) denotes the set of n × n matrices
(a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is
equivalent to A-¹? Justify your answer.
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8
B = 0 7 7
0 -7 7
Working over the field F2 with 2 elements, compute the rank of B as an element
of M2(F2).
(c) Let
1
C
-1 1
[4]
[6]
and consider C as an element of M3(Q). Determine the minimal polynomial
mc(x) and hence, or otherwise, show that C can not be diagonalised.
[7]
(d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write
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[8]
Chapter 9 Solutions
College Algebra (10th Edition)
Ch. 9.1 - For the function f( x )= x1 x , find f( 2 ) and f(...Ch. 9.1 - True or False A function is a relation between two...Ch. 9.1 - Prob. 3AYPCh. 9.1 - True or False The notation a 5 represents the...Ch. 9.1 - True or False If n2 is an integer, then n!=n( n1...Ch. 9.1 - The sequence a 1 =5 , a n =3 a n1 is an example of...Ch. 9.1 - Prob. 7AYPCh. 9.1 - Prob. 8AYPCh. 9.1 - Prob. 9SBCh. 9.1 - Prob. 10SB
Ch. 9.1 - In Problems 9-14, evaluate each factorial...Ch. 9.1 - In Problems 9-14, evaluate each factorial...Ch. 9.1 - In Problems 9-14, evaluate each factorial...Ch. 9.1 - In Problems 9-14, evaluate each factorial...Ch. 9.1 - Prob. 15SBCh. 9.1 - Prob. 16SBCh. 9.1 - Prob. 17SBCh. 9.1 - In Problems 15-26, write down the first five terms...Ch. 9.1 - Prob. 19SBCh. 9.1 - Prob. 20SBCh. 9.1 - In Problems 15-26, write down the first five terms...Ch. 9.1 - Prob. 22SBCh. 9.1 - Prob. 23SBCh. 9.1 - Prob. 24SBCh. 9.1 - Prob. 25SBCh. 9.1 - Prob. 26SBCh. 9.1 - Prob. 27SBCh. 9.1 - Prob. 28SBCh. 9.1 - In Problems 27-34, the given pattern continues....Ch. 9.1 - Prob. 30SBCh. 9.1 - In Problems 27-34, the given pattern continues....Ch. 9.1 - Prob. 32SBCh. 9.1 - In Problems 27-34, the given pattern continues....Ch. 9.1 - Prob. 34SBCh. 9.1 - Prob. 35SBCh. 9.1 - Prob. 36SBCh. 9.1 - Prob. 37SBCh. 9.1 - Prob. 38SBCh. 9.1 - In Problems 35-48, a sequence is defined...Ch. 9.1 - Prob. 40SBCh. 9.1 - In Problems 35-48, a sequence is defined...Ch. 9.1 - Prob. 42SBCh. 9.1 - In Problems 35-48, a sequence is defined...Ch. 9.1 - In Problems 35-48, a sequence is defined...Ch. 9.1 - Prob. 45SBCh. 9.1 - Prob. 46SBCh. 9.1 - Prob. 47SBCh. 9.1 - Prob. 48SBCh. 9.1 - Prob. 49SBCh. 9.1 - Prob. 50SBCh. 9.1 - In Problems 49-58, write out each sum. k=1 n k 2...Ch. 9.1 - Prob. 52SBCh. 9.1 - Prob. 53SBCh. 9.1 - Prob. 54SBCh. 9.1 - Prob. 55SBCh. 9.1 - In Problems 49-58, write out each sum. k=0 n1 (...Ch. 9.1 - Prob. 57SBCh. 9.1 - Prob. 58SBCh. 9.1 - Prob. 59SBCh. 9.1 - Prob. 60SBCh. 9.1 - In Problems 59-68, express each sum using...Ch. 9.1 - Prob. 62SBCh. 9.1 - Prob. 63SBCh. 9.1 - Prob. 64SBCh. 9.1 - Prob. 65SBCh. 9.1 - Prob. 66SBCh. 9.1 - Prob. 67SBCh. 9.1 - Prob. 68SBCh. 9.1 - Prob. 69SBCh. 9.1 - Prob. 70SBCh. 9.1 - In Problems 69-80, find the sum of each sequence. ...Ch. 9.1 - Prob. 72SBCh. 9.1 - Prob. 73SBCh. 9.1 - Prob. 74SBCh. 9.1 - Prob. 75SBCh. 9.1 - Prob. 76SBCh. 9.1 - In Problems 69-80, find the sum of each sequence. ...Ch. 9.1 - Prob. 78SBCh. 9.1 - Prob. 79SBCh. 9.1 - Prob. 80SBCh. 9.1 - Credit Card Debt John has a balance of 3000 on his...Ch. 9.1 - Prob. 82AECh. 9.1 - Car Loans Phil bought a car by taking out a loan...Ch. 9.1 - Prob. 84AECh. 9.1 - Prob. 85AECh. 9.1 - Fibonacci Sequence Let u n = ( 1+ 5 ) n ( 1 5 ) n...Ch. 9.1 - Prob. 87AECh. 9.1 - Prob. 88AECh. 9.1 - Approximating f(x) =e x In calculus, it can be...Ch. 9.1 - Approximating f(x) =e x Refer to Problem 89. a....Ch. 9.1 - 91. Bode s Law In 1772, Johann Bode published the...Ch. 9.1 - Show that 1+2+...+( n1 )+n= n( n+1 ) 2 [Hint: Let]...Ch. 9.1 - Computing Square Roots A method for approximating...Ch. 9.1 - Prob. 94AECh. 9.1 - Prob. 95AECh. 9.1 - Prob. 96AECh. 9.1 - Prob. 97AECh. 9.1 - For the sequence given in problem 97, show that u...Ch. 9.1 - For the sequence given in problem 97, show that u...Ch. 9.1 - 100. Investigate various applications that lead to...Ch. 9.1 - Write a paragraph that explains why the numbers...Ch. 9.1 - If 2500 is invested at 3 compounded monthly, find...Ch. 9.1 - Solve the inequality: x 3 + x 2 16x160 .Ch. 9.1 - Prob. 104RYKCh. 9.1 - Prob. 105RYKCh. 9.2 - In a(n) ________ sequence, the difference between...Ch. 9.2 - True or False For an arithmetic sequence { a n }...Ch. 9.2 - Prob. 3CVCh. 9.2 - Prob. 4CVCh. 9.2 - Prob. 5CVCh. 9.2 - If a n =2n+7 is the n th term of an arithmetic...Ch. 9.2 - show that each sequence is arithmetic. Find the...Ch. 9.2 - show that each sequence is arithmetic. Find the...Ch. 9.2 - show that each sequence is arithmetic. Find the...Ch. 9.2 - show that each sequence is arithmetic. Find the...Ch. 9.2 - show that each sequence is arithmetic. Find the...Ch. 9.2 - show that each sequence is arithmetic. Find the...Ch. 9.2 - Prob. 13SBCh. 9.2 - show that each sequence is arithmetic. Find the...Ch. 9.2 - Prob. 15SBCh. 9.2 - Prob. 16SBCh. 9.2 - In Problems 17-24, find the nth term of the...Ch. 9.2 - In Problems 17-24, find the n th term of the...Ch. 9.2 - Prob. 19SBCh. 9.2 - Prob. 20SBCh. 9.2 - Prob. 21SBCh. 9.2 - Prob. 22SBCh. 9.2 - In Problems 17-24, find the n th term of the...Ch. 9.2 - Prob. 24SBCh. 9.2 - In Problems 25-30, find the indicated term in each...Ch. 9.2 - Prob. 26SBCh. 9.2 - In Problems 25-30, find the indicated term in each...Ch. 9.2 - Prob. 28SBCh. 9.2 - In Problems 25-30, find the indicated term in each...Ch. 9.2 - Prob. 30SBCh. 9.2 - Prob. 31SBCh. 9.2 - Prob. 32SBCh. 9.2 - Prob. 33SBCh. 9.2 - Prob. 34SBCh. 9.2 - Prob. 35SBCh. 9.2 - Prob. 36SBCh. 9.2 - In Problems 31-38, find the first term and the...Ch. 9.2 - Prob. 38SBCh. 9.2 - Prob. 39SBCh. 9.2 - Prob. 40SBCh. 9.2 - Prob. 41SBCh. 9.2 - Prob. 42SBCh. 9.2 - Prob. 43SBCh. 9.2 - Prob. 44SBCh. 9.2 - Prob. 45SBCh. 9.2 - Prob. 46SBCh. 9.2 - In Problems 39-56, find each sum. 73+78+83+88++558Ch. 9.2 - Prob. 48SBCh. 9.2 - Prob. 49SBCh. 9.2 - Prob. 50SBCh. 9.2 - In Problems 39-56, find each sum. n1 80 ( 2n5 )Ch. 9.2 - n=1 90 ( 32bn )Ch. 9.2 - n=1 100 ( 6 1 2 n )Ch. 9.2 - Prob. 54SBCh. 9.2 - Prob. 55SBCh. 9.2 - Prob. 56SBCh. 9.2 - Prob. 57SBCh. 9.2 - Prob. 58SBCh. 9.2 - Prob. 59SBCh. 9.2 - Prob. 60SBCh. 9.2 - Prob. 61SBCh. 9.2 - Prob. 62SBCh. 9.2 - Prob. 63SBCh. 9.2 - Prob. 64SBCh. 9.2 - Prob. 65SBCh. 9.2 - Prob. 66SBCh. 9.2 - Seats in an Amphitheater An outdoor amphitheater...Ch. 9.2 - Prob. 68SBCh. 9.2 - Prob. 69SBCh. 9.2 - Prob. 70DWCh. 9.2 - Prob. 71DWCh. 9.2 - Prob. 72RYKCh. 9.2 - Prob. 73RYKCh. 9.2 - Prob. 74RYKCh. 9.2 - Prob. 75RYKCh. 9.3 - If 1000 is invested at 4 per annum compounded...Ch. 9.3 - Prob. 2AYPCh. 9.3 - Prob. 3CVCh. 9.3 - Prob. 4CVCh. 9.3 - Prob. 5CVCh. 9.3 - True or False A geometric sequence may be defined...Ch. 9.3 - Prob. 7CVCh. 9.3 - Prob. 8CVCh. 9.3 - In Problems 9-18, show that each sequence is...Ch. 9.3 - Prob. 10SBCh. 9.3 - Prob. 11SBCh. 9.3 - Prob. 12SBCh. 9.3 - Prob. 13SBCh. 9.3 - Prob. 14SBCh. 9.3 - Prob. 15SBCh. 9.3 - Prob. 16SBCh. 9.3 - Prob. 17SBCh. 9.3 - Prob. 18SBCh. 9.3 - In Problems 19-26, find the fifth term and the nth...Ch. 9.3 - Prob. 20SBCh. 9.3 - Prob. 21SBCh. 9.3 - Prob. 22SBCh. 9.3 - Prob. 23SBCh. 9.3 - Prob. 24SBCh. 9.3 - Prob. 25SBCh. 9.3 - Prob. 26SBCh. 9.3 - Prob. 27SBCh. 9.3 - Prob. 28SBCh. 9.3 - In Problems 27- 32, find the indicated term of...Ch. 9.3 - Prob. 30SBCh. 9.3 - Prob. 31SBCh. 9.3 - Prob. 32SBCh. 9.3 - Prob. 33SBCh. 9.3 - Prob. 34SBCh. 9.3 - Prob. 35SBCh. 9.3 - Prob. 36SBCh. 9.3 - Prob. 37SBCh. 9.3 - Prob. 38SBCh. 9.3 - In Problems 33-40, find the nth term a n of each...Ch. 9.3 - Prob. 40SBCh. 9.3 - Prob. 41SBCh. 9.3 - Prob. 42SBCh. 9.3 - Prob. 43SBCh. 9.3 - Prob. 44SBCh. 9.3 - Prob. 45SBCh. 9.3 - Prob. 46SBCh. 9.3 - Prob. 47SBCh. 9.3 - Prob. 48SBCh. 9.3 - For Problems 47-52, use a graphing utility to find...Ch. 9.3 - Prob. 50SBCh. 9.3 - Prob. 51SBCh. 9.3 - Prob. 52SBCh. 9.3 - Prob. 53SBCh. 9.3 - Prob. 54SBCh. 9.3 - Prob. 55SBCh. 9.3 - Prob. 56SBCh. 9.3 - In Problems 53-68, determine whether each infinite...Ch. 9.3 - In Problems 53-68, determine whether each infinite...Ch. 9.3 - In Problems 53-68, determine whether each infinite...Ch. 9.3 - Prob. 60SBCh. 9.3 - Prob. 61SBCh. 9.3 - Prob. 62SBCh. 9.3 - Prob. 63SBCh. 9.3 - Prob. 64SBCh. 9.3 - Prob. 65SBCh. 9.3 - Prob. 66SBCh. 9.3 - In Problems 53-68, determine whether each infinite...Ch. 9.3 - Prob. 68SBCh. 9.3 - In Problems 69-82, determine whether the given...Ch. 9.3 - Prob. 70MPCh. 9.3 - Prob. 71MPCh. 9.3 - Prob. 72MPCh. 9.3 - Prob. 73MPCh. 9.3 - Prob. 74MPCh. 9.3 - Prob. 75MPCh. 9.3 - Prob. 76MPCh. 9.3 - Prob. 77MPCh. 9.3 - Prob. 78MPCh. 9.3 - Prob. 79MPCh. 9.3 - Prob. 80MPCh. 9.3 - Prob. 81MPCh. 9.3 - Prob. 82MPCh. 9.3 - Prob. 83AECh. 9.3 - Prob. 84AECh. 9.3 - Prob. 85AECh. 9.3 - Prob. 86AECh. 9.3 - Pendulum Swings Initially, a pendulum swings...Ch. 9.3 - Prob. 88AECh. 9.3 - Retirement Christine contributes 100 each month to...Ch. 9.3 - Prob. 90AECh. 9.3 - Prob. 91AECh. 9.3 - Prob. 92AECh. 9.3 - Prob. 93AECh. 9.3 - Prob. 94AECh. 9.3 - Grains of Wheat on a Chess Board In an old fable,...Ch. 9.3 - Prob. 96AECh. 9.3 - Multiplier Suppose that, throughout the U.S....Ch. 9.3 - Multiplier Refer to Problem 97. Suppose that the...Ch. 9.3 - Prob. 99AECh. 9.3 - Prob. 100AECh. 9.3 - A Rich Man’s Promise A rich man promises to give...Ch. 9.3 - Prob. 102AECh. 9.3 - Prob. 103DWCh. 9.3 - Prob. 104DWCh. 9.3 - Critical Thinking You have just signed a 7-year...Ch. 9.3 - Prob. 106DWCh. 9.3 - Prob. 107DWCh. 9.3 - Prob. 108DWCh. 9.3 - Prob. 109DWCh. 9.3 - Describe the similarities and differences between...Ch. 9.3 - Prob. 111RYKCh. 9.3 - Find the inverse of the nonsingular matrix: [ 1 0...Ch. 9.3 - Prob. 113RYKCh. 9.3 - Prob. 114RYKCh. 9.4 - In Problems 1-22, use the Principle of...Ch. 9.4 - Prob. 2SBCh. 9.4 - In Problems 1-22, use the Principle of...Ch. 9.4 - In Problems 1-22, use the Principle of...Ch. 9.4 - In Problems 1-22, use the Principle of...Ch. 9.4 - Prob. 6SBCh. 9.4 - Prob. 7SBCh. 9.4 - Prob. 8SBCh. 9.4 - Prob. 9SBCh. 9.4 - Prob. 10SBCh. 9.4 - Prob. 11SBCh. 9.4 - Prob. 12SBCh. 9.4 - Prob. 13SBCh. 9.4 - Prob. 14SBCh. 9.4 - Prob. 15SBCh. 9.4 - Prob. 16SBCh. 9.4 - Prob. 17SBCh. 9.4 - Prob. 18SBCh. 9.4 - In Problems 1-22, use the Principle of...Ch. 9.4 - Prob. 20SBCh. 9.4 - Prob. 21SBCh. 9.4 - Prob. 22SBCh. 9.4 - Prob. 23AECh. 9.4 - Prob. 24AECh. 9.4 - In Problems 23-27, prove each statement. ab is a...Ch. 9.4 - Prob. 26AECh. 9.4 - Prob. 27AECh. 9.4 - Prob. 28AECh. 9.4 - Prob. 29AECh. 9.4 - Prob. 30AECh. 9.4 - Prob. 31AECh. 9.4 - Prob. 32AECh. 9.4 - Prob. 33AECh. 9.4 - How would you explain the Principle of...Ch. 9.4 - Prob. 35RYKCh. 9.4 - Prob. 36RYKCh. 9.4 - Prob. 37RYKCh. 9.4 - Prob. 38RYKCh. 9.5 - The ______ ________ is a triangular display of the...Ch. 9.5 - Prob. 2CVCh. 9.5 - Prob. 3CVCh. 9.5 - Prob. 4CVCh. 9.5 - In Problems 5-16, evaluate each expression. ( 5 3...Ch. 9.5 - Prob. 6SBCh. 9.5 - Prob. 7SBCh. 9.5 - Prob. 8SBCh. 9.5 - Prob. 9SBCh. 9.5 - Prob. 10SBCh. 9.5 - Prob. 11SBCh. 9.5 - Prob. 12SBCh. 9.5 - In Problems 5-16, evaluate each expression. ( 55...Ch. 9.5 - In Problems 5-16, evaluate each expression. ( 60...Ch. 9.5 - In Problems 5-16, evaluate each expression. ( 47...Ch. 9.5 - In Problems 5-16, evaluate each expression. ( 37...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 17-28, expand each expression using...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - In Problems 29-42, use the Binomial Theorem to...Ch. 9.5 - Use the Binomial Theorem to find the numerical...Ch. 9.5 - Use the Binomial Theorem to find the numerical...Ch. 9.5 - Prob. 45SBCh. 9.5 - Prob. 46SBCh. 9.5 - Prob. 47SBCh. 9.5 - Prob. 48SBCh. 9.5 - Prob. 49SBCh. 9.5 - Prob. 50SBCh. 9.5 - Prob. 51RYKCh. 9.5 - Prob. 52RYKCh. 9.5 - Prob. 53RYKCh. 9.5 - Prob. 54RYK
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