Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 12, Problem 4CR
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For problems 11, 12, and 13. Suppose A =
11) Find Col(A)
12) Find Null(A)
13) Is it possible to find Eigenvalues for matrix A?
(second picture is the previous problem the question is referring to, it asked to find the eigenvalues which are -2, 0, and 2)
Problem 5. Show from the eigenvalues that if A is positive definite, so is A² and so is A-¹.
Chapter 12 Solutions
Advanced Engineering Mathematics
Ch. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Prob. 10E
Ch. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 50ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - Prob. 9ECh. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 13ECh. 12.6 - Prob. 3ECh. 12.6 - Prob. 4ECh. 12.6 - Prob. 5ECh. 12.6 - Prob. 6ECh. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - Prob. 13ECh. 12.6 - Prob. 14ECh. 12.6 - Prob. 15ECh. 12.6 - Prob. 16ECh. 12.6 - Prob. 17ECh. 12.6 - Prob. 18ECh. 12.6 - Prob. 19ECh. 12.6 - Prob. 20ECh. 12.6 - Prob. 21ECh. 12.6 - Prob. 22ECh. 12.6 - Prob. 23ECh. 12.6 - Prob. 24ECh. 12 - Prob. 1CRCh. 12 - Prob. 2CRCh. 12 - Prob. 3CRCh. 12 - Prob. 4CRCh. 12 - Prob. 5CRCh. 12 - Prob. 6CRCh. 12 - Prob. 11CRCh. 12 - Prob. 12CRCh. 12 - Prob. 13CRCh. 12 - Prob. 14CRCh. 12 - Prob. 16CRCh. 12 - Prob. 17CRCh. 12 - Prob. 19CRCh. 12 - Prob. 20CRCh. 12 - Prob. 21CRCh. 12 - Prob. 22CRCh. 12 - Prob. 23CRCh. 12 - Prob. 24CRCh. 12 - Prob. 25CR
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- Please help. Problem 6 involves finding the eigenvalues. Thank you.arrow_forwardProblem 2 5a – 7 -10a + 47 -10a + 41 Let M(a) = -a + 2 2a + 8 2a – 1 2а-4 -4a + 14 -4a + 17 (a) Find all values of a for which M(a) has some 2-dimensional eigenspace (for some eigenvalue). You might find it useful to know that 3 is an eigenvalue of M(a) for all values of a. (b) For each value that you find in (a), find a matrix P for which P- M(a)P = D, where D is diagonal. (c) Find all values of a for which M(a) is diagonalizable.arrow_forwardQ8.7 You have been problem: :2 x been given the following boundry value. + (49 + x)y=0₂y(e¹) = 0; y (1² y! - 13 xy² + (49 + (1)=0 Find the eigenfunctions for it. In the eigenfunction take the or general solution to be 1. Write a symbolic function decimals in your answer.. your of x: do not have ans wer as anyarrow_forward
- Need help with PDE finding eigenvalues and eigenfunctions of the given Sturm-Liouville Problemsarrow_forward9. 6. Find the three dishinct real eigenvalues of the matry B=-3 |-2arrow_forward. Let A = 2 150 00 00 0 52000 CATL co 9 11 -1 0 -13 7 2 0 3 . Find all the eigenvalues of A5. Justify your answer.arrow_forward
- Problem 10. Suppose that x is an eigenvector for a matrix A with eigenvalue A = -2. Compute A5x. (a) -10x (b) -32x (c) 3x (d) C -2x (e) None of the above DELLarrow_forwardProblem 1. a₂x² + +anx". Then (a) (b) If A is diagonalizable, that is A = QDQ¹. Assume a polynomial f(x) = a₁ + a₁x + (c) Prove that f(A) = Q (f(2₂) 0 0 f(2₂) 0 0 0 8 ƒ(2₂)) Q¹, where : eigenvalues of A. If f(A) = B, where A and B are both n x n diagonalizable matrices and have identical eigenvectors, then pro that f(ai) = λbi, in which ai and Abi are the eigenvalues of A and B. -7 6 Apply (b) to find the solutions of A that satisfies A² -3A+I = 9. -12 11arrow_forward. If A₁ and A₂ are the eigenvalues of A 30 B 16 C 20 D 36 3 then X² + x² =arrow_forward
- 2. The eigenvalues of the matrix A = are 5 and -2 (you are not asked to prove this, you can use it without proof). For each real number x, find the rank of the matrix x - 1 -3 xI - A = -4arrow_forwardc). Find the Green's function corresponding the the Sturm-Liouville problem found in part a).- COarrow_forwardProblem 15.2. Let A be any complex n X n matrix. Prove that if A has the eigenvalue 0 with multiplicity n, then A" = 0. Give an example of a matrix A such that A" = 0 but A 0arrow_forward
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