Show that if A? is the zero matrix, then the only eigenvalue of A is 0. ..... Choose the correct answer below. A. If Ax = Ax for some i+0, then A² = 22 +0. Thus, each eigenvalue of A is zero. B. If Ax = Ax for some x+0, then (A-Al)x = 0. Since x is nonzero, A must be zero. Thus, each eigenvalue of A is zero. C. If Ax = ix for some x = 0, then A?x = Ax = ix = 0. Thus, each eigenvalue of A is zero. O D. If Ax = Ax for some x+0, then Ox = A'x= A(Ax) = A(x) = Ax =1?x= 0. Since x is nonzero, A must be zero. Thus, each eigenvalue of A is zero.

Show that if A? is the zero matrix, then the only eigenvalue of A is 0. ..... Choose the correct answer below. A. If Ax = Ax for some i+0, then A² = 22 +0. Thus, each eigenvalue of A is zero. B. If Ax = Ax for some x+0, then (A-Al)x = 0. Since x is nonzero, A must be zero. Thus, each eigenvalue of A is zero. C. If Ax = ix for some x = 0, then A?x = Ax = ix = 0. Thus, each eigenvalue of A is zero. O D. If Ax = Ax for some x+0, then Ox = A'x= A(Ax) = A(x) = Ax =1?x= 0. Since x is nonzero, A must be zero. Thus, each eigenvalue of A is zero.

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

Show that if A? is the zero matrix, then the only eigenvalue of A is 0.
.....
Choose the correct answer below.
A. If Ax = Ax for some i+0, then A² = 22 +0. Thus, each eigenvalue of A is zero.
B. If Ax = Ax for some x+0, then (A-Al)x = 0. Since x is nonzero, A must be zero. Thus, each eigenvalue of A is zero.
C. If Ax = ix for some x = 0, then A?x = Ax = ix = 0. Thus, each eigenvalue of A is zero.
O D. If Ax = Ax for some x+0, then Ox = A'x= A(Ax) = A(x) = NAx =1?x= 0. Since x is nonzero, A must be zero. Thus, each eigenvalue of A is zero.

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