Suppose that for a 2x2 matrix \( A \), \( A\vec{v} = 3\vec{v} \) for \( \vec{v} = \begin{bmatrix} -1 \\ -1 \end{bmatrix} \).- How is the pair (3, \( \vec{v} \)) called for a matrix \( A \)?Suppose further that the only non-zero vectors \( x \), for which \( Ax = rx \) for some \( r \), must be multiples of \( \vec{v} \) above.- What more can you now say about the number \( r = 3 \)?Suppose further that \( A\vec{w} = 3\vec{w} = \vec{w} \) for \( \vec{w} = \begin{bmatrix} -3 \\ -1 \end{bmatrix} \). Write down the general solution of the differential equation\[ x'(t) = Ax \]

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Suppose that for a 2 x 2 matrix A, AF= 35 for 7 = • How is the pair (3, 7) called for a matrix A? Suppose further that the only non-zero vectors z, for which Ar = rr for some r, must be multiples of r above. • What more can you now saw about the number r= 3? Suppose further that Au-3u i for tw = Write down the general solution of the differential equation x'(1) = Ax CS Scanned with CamScanner

Suppose that for a 2 x 2 matrix A, AF= 35 for 7 = • How is the pair (3, 7) called for a matrix A? Suppose further that the only non-zero vectors z, for which Ar = rr for some r, must be multiples of r above. • What more can you now saw about the number r= 3? Suppose further that Au-3u i for tw = Write down the general solution of the differential equation x'(1) = Ax CS Scanned with CamScanner

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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