Suppose that for a 2 x 2 matrix A, AŬ= 3õ for ū = How is the pair (3, v) called for a matrix A? Suppose further that the only non-zero vectors r, for which Ar = rx for some r, must be multiples of v above. What more can you now saw about the number r = 3? Suppose further that Aw – 3w = õ for w = Write down the general solution of the differential equation x'(t) = Ax

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Suppose that for a 2 x 2 matrix A, AU = 3u for ū =
• How is the pair (3, 0) called for a matrix A?
Suppose further that the only non-zero vectors r, for which Ar = rz for some r, must
be multiples of v above.
• What more can you now saw about the number r =
3?
Suppose further that Au-3w = ở for w =
Write down the general solution of
the differential equation
x'(t) = Ax
Transcribed Image Text:Suppose that for a 2 x 2 matrix A, AU = 3u for ū = • How is the pair (3, 0) called for a matrix A? Suppose further that the only non-zero vectors r, for which Ar = rz for some r, must be multiples of v above. • What more can you now saw about the number r = 3? Suppose further that Au-3w = ở for w = Write down the general solution of the differential equation x'(t) = Ax
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