Consider the matrix AB3 A = = Suppose that a matrix B is diagonalizable and shares the same eigenvectors as matrix A. Given that -7 -6 9 0 8 0 0 0 -4a³-24c³ -4a³ - 16c³ 0 6a³ +24c³ 6a³ +16c³ 0 0 0 -276³] Compute the eigenvalues of matrix B, in terms of a, b and c, of the corresponding eigenvectors.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Topic: MATHEMATICAL METHODS I
Consider the matrix
-7 9
A = -6 8
00
AB3 =
Suppose that a matrix B is diagonalizable and shares the same eigenvectors as matrix
A. Given that
0
0
[-4a³-24c³
-4a³ - 16c3
0
6a³ +24c³
6a³ 16c³
0
0
0
-276³
Compute the eigenvalues of matrix B, in terms of a, b and c, of the corresponding
eigenvectors.
Transcribed Image Text:Topic: MATHEMATICAL METHODS I Consider the matrix -7 9 A = -6 8 00 AB3 = Suppose that a matrix B is diagonalizable and shares the same eigenvectors as matrix A. Given that 0 0 [-4a³-24c³ -4a³ - 16c3 0 6a³ +24c³ 6a³ 16c³ 0 0 0 -276³ Compute the eigenvalues of matrix B, in terms of a, b and c, of the corresponding eigenvectors.
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