Assume that A and B are in M(C). Show that if Bis invertible, then there exists a scalarCE C suchthat A + cB is not invertible.Hint: First, show that det (A + tB)- det(B) - det (AB+ tl). Next, use the fundamental theoremmust have a complex eigenvalue A. Conclude that A+ cBis-1of algebra to argue that the matrix ABnot invertible for c=A.

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Assume that A and B are in Ma(C). Show that if Bis invertible, then there exists a scalar e e C such that A+ cB is not invertible. Hint: First, show that det(A+ tB)- det (B) - det (AB + tla). Next, use the fundamental theorem of algebra to argue that the matrix AB not invertible for c must have a complex eigenvalue . Conclude that A+ cBis A.

Assume that A and B are in Ma(C). Show that if Bis invertible, then there exists a scalar e e C such that A+ cB is not invertible. Hint: First, show that det(A+ tB)- det (B) - det (AB + tla). Next, use the fundamental theorem of algebra to argue that the matrix AB not invertible for c must have a complex eigenvalue . Conclude that A+ cBis A.

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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