Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
14th Edition
ISBN: 9780134668574
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker
Publisher: PEARSON
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Chapter B.2, Problem 15E
To determine
To find: The terms
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Let
2
A =
4
3
-4
0
1
(a) Show that v =
eigenvalue.
()
is an eigenvector of A and find the corresponding
(b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a)
may be useful.
(c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces.
(d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.
(c) Let
6
0 0
A =
-10 4 8
5 1 2
(i) Find the characteristic polynomial of A and factorise it.
(ii) Determine all eigenvalues of A and find bases for the corresponding
eigenspaces.
(iii) Is A diagonalisable? Give reasons for your answer.
Chapter B.2 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Ch. B.2 - Which of the following can be the first four terms...Ch. B.2 - (A)If the 1st and 15th terms of an arithmetic...Ch. B.2 - Prob. 3MPCh. B.2 - MATCHED PROBLEM 4 Find the sum of all the odd...Ch. B.2 - Find the sum of the first eight terms of the...Ch. B.2 - Repeat Example 6 with a loan of 6,000 over 5...Ch. B.2 - Repeat Example 7 with a tax rebate of 2,000....Ch. B.2 - In Problems 1 and 2, determine whether the...Ch. B.2 - In Problems 1 and 2, determine whether the...Ch. B.2 - In Problems 38, determine whether the finite...
Ch. B.2 - In Problems 38, determine whether the finite...Ch. B.2 - Prob. 5ECh. B.2 - In Problems 38, determine whether the finite...Ch. B.2 - In Problems 38, determine whether the finite...Ch. B.2 - In Problems 38, determine whether the finite...Ch. B.2 - Let a1, a2, a3, , an, be an arithmetic sequence....Ch. B.2 - Let a1, a2, a3, , an, be an arithmetic sequence....Ch. B.2 - Prob. 11ECh. B.2 - Let a1, a2, a3, , an, be an arithmetic sequence....Ch. B.2 - Let a1, a2, a3, , an, be an arithmetic sequence....Ch. B.2 - Prob. 14ECh. B.2 - Prob. 15ECh. B.2 - Let a1, a2, a3, , an, be a geometric sequence. In...Ch. B.2 - Prob. 17ECh. B.2 - Let a1, a2, a3, , an, be a geometric sequence. In...Ch. B.2 - Prob. 19ECh. B.2 - Let a1, a2, a3, , an, be a geometric sequence. In...Ch. B.2 - Let a1, a2, a3, , an, be a geometric sequence. In...Ch. B.2 - Let a1, a2, a3, , an, be a geometric sequence. In...Ch. B.2 - Prob. 23ECh. B.2 - Let a1, a2, a3, , an, be a geometric sequence. In...Ch. B.2 - S41=k=141(3k+3)=?Ch. B.2 - Prob. 26ECh. B.2 - S8=k=18(2)k1=?Ch. B.2 - S8=k=182k=?Ch. B.2 - Find the sum of all the odd integers between 12...Ch. B.2 - Find the sum of all the even integers between 23...Ch. B.2 - Find the sum of each infinite geometric sequence...Ch. B.2 - Repeat Problem 31 for: (A)16, 4, 1, (B)1, 3, 9, ...Ch. B.2 - Find f(1)+f(2)+f(3)++f(50) if f(x) = 2x 3.Ch. B.2 - Find g(1)+g(2)+g(3)++g(100) if g(t) = 18 3t.Ch. B.2 - Find f(1)+f(2)++f(10) if f(x)=(12)x.Ch. B.2 - Find g(1)+g(2)++g(10) if g(x) = 2x.Ch. B.2 - Prob. 37ECh. B.2 - Show that the sum of the first n even positive...Ch. B.2 - If r = 1, neither the first form nor the second...Ch. B.2 - Prob. 40ECh. B.2 - Does there exist a finite arithmetic series with...Ch. B.2 - Does there exist a finite arithmetic series with...Ch. B.2 - Does there exist a infinite geometric series with...Ch. B.2 - Does there exist an infinite geometric series with...Ch. B.2 - Loan repayment. If you borrow 4,800 and repay the...Ch. B.2 - Loan repayment. If you borrow 5,400 and repay the...Ch. B.2 - Economy stimulation. The government, through a...Ch. B.2 - Economy stimulation. Due to reduced taxes, a...Ch. B.2 - Compound interest. If 1,000 is invested at 5%...Ch. B.2 - Compound interest. If P is invested at 100r%...
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