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If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as p(x) = p₁(x)p₂(x) then it can be proved that p(A) = P₁(A)p2(A) for an arbitrary square matrix A. Verify this statement for polynomials p(x) = x² − 9, P₁(x)=x+3, p₂(x) = x − 3.

If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as p(x) = p₁(x)p₂(x) then it can be proved that p(A) = P₁(A)p2(A) for an arbitrary square matrix A. Verify this statement for polynomials p(x) = x² − 9, P₁(x)=x+3, p₂(x) = x − 3.

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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If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁ (x) and p₂(x) as p(x) = P₁(x)p2(x) then it can be proved that p(A) = P₁(A)p2(A) for an arbitrary square matrix A. Verify this statement for polynomials p(x)=x²-9, P₁(x) = x+3, p2(x) = x - 3.
Transcribed Image Text:If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁ (x) and p₂(x) as p(x) = P₁(x)p2(x) then it can be proved that p(A) = P₁(A)p2(A) for an arbitrary square matrix A. Verify this statement for polynomials p(x)=x²-9, P₁(x) = x+3, p2(x) = x - 3.
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