In Exercises 1-6, show that
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Linear Algebra: A Modern Introduction
- In Exercises 7-12, show that is an eigenvector of A and find one eigenvector corresponding to this eigenvalue. A=[311111420],=2arrow_forwardConsider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two distinct real eigenvalues, one real eigenvalue, and no real eigenvalues.arrow_forwardIn Exercises 19-22, find the eigenvalues and the corresponding eigenvectors of the matrix. [7223]arrow_forward
- In Exercises 23-26, use the method of Example 4.5 to find all of the eigenvalues of the matrix A. Give bases for each of the corresponding eigenspaces. 25.arrow_forwardIn Exercises 31-34, find all of the eigenvalues of the matrix A over the indicated p. A=[3140]over5arrow_forwardDefine T:P2P2 by T(a0+a1x+a2x2)=(2a0+a1a2)+(a1+2a2)xa2x2. Find the eigenvalues and the eigenvectors of T relative to the standard basis {1,x,x2}.arrow_forward
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