The 3 x 3 matrix B is known to to have eigenvalues 0, 1, and 2. Is this information enough to determine the following (if yes, give the answer and explain; if no, explain why not): (a) The rank B; (b) The determinant of BTB; (c) the eigenvalues of BT B; (d) The eigenvalues of (B2 + I)-1.

The 3 x 3 matrix B is known to to have eigenvalues 0, 1, and 2. Is this information enough to determine the following (if yes, give the answer and explain; if no, explain why not): (a) The rank B; (b) The determinant of BTB; (c) the eigenvalues of BT B; (d) The eigenvalues of (B2 + I)-1.

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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Question

The 3 x 3 matrix B is known to to have eigenvalues 0, 1, and 2. Is this information enough
to determine the following (if yes, give the answer and explain; if no, explain why not):
(a) The rank B;
(b) The determinant of BTB;
(c) the eigenvalues of BT B;
(d) The eigenvalues of (B? + I)-1.

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