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4. Let T E L(C³) be defined by -5 1 -5 Tr= |-32 4 -17 z, -11 1 Find a basis of C³ such that the matrix representation of T with respect to this basis is block diagonal with blocks that are upper triangular and where the diagonal entries on a single block are identical. You may use the fact that 6 and –3 are the only eigenvalues of T and that –3 has multiplicity two. zE C". 1 Explicitly show that the matrix representation is the correct form by computing T applied to the basis vectors and writing the results as coordinates with respect to the basis.

4. Let T E L(C³) be defined by -5 1 -5 Tr= |-32 4 -17 z, -11 1 Find a basis of C³ such that the matrix representation of T with respect to this basis is block diagonal with blocks that are upper triangular and where the diagonal entries on a single block are identical. You may use the fact that 6 and –3 are the only eigenvalues of T and that –3 has multiplicity two. zE C". 1 Explicitly show that the matrix representation is the correct form by computing T applied to the basis vectors and writing the results as coordinates with respect to the basis.

Advanced Engineering Mathematics
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. Let T E L(C®) be defined by -5 1 -5 Tx = |-32 4 -17 a, -11 1 x € C³. 1 Find a basis of C³ such that the matrix representation of T with respect to this basis is block diagonal with blocks that are upper triangular and where the diagonal entries on a single block are identical. You may use the fact that 6 and –3 are the only eigenvalues of T and that –3 has multiplicity two. Explicitly show that the matrix representation is the correct form by computing T applied to the basis vectors and writing the results as coordinates with respect to the basis.
Transcribed Image Text:4. Let T E L(C®) be defined by -5 1 -5 Tx = |-32 4 -17 a, -11 1 x € C³. 1 Find a basis of C³ such that the matrix representation of T with respect to this basis is block diagonal with blocks that are upper triangular and where the diagonal entries on a single block are identical. You may use the fact that 6 and –3 are the only eigenvalues of T and that –3 has multiplicity two. Explicitly show that the matrix representation is the correct form by computing T applied to the basis vectors and writing the results as coordinates with respect to the basis.
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