13 920 31 21-4Let 6and let AIs 6 in the range of the linear transformation + Aa? Why or why not?=-2 3 05

Answered: -1 1 3 9 0 3 1 2 -2 3 0 3 and let A = 1…

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

1
3 9
2
0 3
1 2
1
-4
Let 6
and let A
Is 6 in the range of the linear transformation + Aa? Why or why not?
=
-2 3 0
5

Expert Solution

Step 1

According to the given information it is required to check if the given vector b lies in the range of the linear transformation from x to Ax, where

$\vec{b} = [\begin{matrix} - 1 \\ 3 \\ - 1 \\ 4 \end{matrix}], and A = [\begin{matrix} 1 & 3 & 9 & 2 \\ 1 & 0 & 3 & - 4 \\ 0 & 1 & 2 & 3 \\ - 2 & 3 & 0 & 5 \end{matrix}]$

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