Problem 1. he matrix -1 C = -8 -5 -18 -1 -5 has two distinct eigenvalues with A < A2. The smaller eigenvalue A = has multiplicity and the dimension of the corresponding eigenspace is The larger eigenvalue A2 = has multiplicity and the dimension of the corresponding eigenspace is Is the matrix C diagonalizable? choose Note: You can earn partial credit on this problem. preview answers

Problem 1. he matrix -1 C = -8 -5 -18 -1 -5 has two distinct eigenvalues with A < A2. The smaller eigenvalue A = has multiplicity and the dimension of the corresponding eigenspace is The larger eigenvalue A2 = has multiplicity and the dimension of the corresponding eigenspace is Is the matrix C diagonalizable? choose Note: You can earn partial credit on this problem. preview answers

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. -2 2 A =| 2 2 -2 4 Step 4: Find a possible basis for the larger eigenvalue 12. There are infinitely many possibilities but we will restrict ourselves to fill in only either 1 or 0. In case you need only one vector, fill the vector on the left with numbers as instructed and fill in each of the entries of the vector on the right with X's (Capital X). Answer: a basis for the eigenspace corresponding to the larger eigenvalue 12 is where a= , b= C= d= e= 2.
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3. 3 -3 Consider the matrix A = |0 4 0 For this matrix: -1 -1 1 Part (a): Find all of its eigenvalues. Part (b): Find each eigenspace and a basis for it. (Clearly indicate what is the eigenspace and what is its basis.) Part (c): Find the algebraic and geometric multiplicity of each eigenvalue. Part (d): Determine (with explanation) whether or not this matrix is diagonalizable. (You do not have to diagonalize it if it is.)