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Suppose A € M3 (R) and that A is diagonalizable. Suppose that A₁, A2, and A3 are the three eigenvalues of A. These may or may not be distinct. Show that det A = A₁ A2 A3. Make sure to submit a clear, complete, and detailed proof of this.

Suppose A € M3 (R) and that A is diagonalizable. Suppose that A₁, A2, and A3 are the three eigenvalues of A. These may or may not be distinct. Show that det A = A₁ A2 A3. Make sure to submit a clear, complete, and detailed proof of this.

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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Please give a clear and complete solution. Linear algebra and differential equations

Suppose A € M3 (R) and that A is diagonalizable. Suppose that A₁, A2, and A3 are the three eigenvalues of A. These may or may not be distinct. Show that det A = X₁ X₂ X3. Make sure to submit a clear, complete, and detailed proof of this.
Transcribed Image Text:Suppose A € M3 (R) and that A is diagonalizable. Suppose that A₁, A2, and A3 are the three eigenvalues of A. These may or may not be distinct. Show that det A = X₁ X₂ X3. Make sure to submit a clear, complete, and detailed proof of this.
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