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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![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
\[ x'(t) = Ax \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d6f30ef-51d6-4f6d-808a-d01cff83fa92%2F41f29fac-13e4-442b-bb47-23e16b24d547%2F08003e06_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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