1 0 -43 -2| and 6Let ADenote the columns of A by d1, å2, åz , and let W = Span{ă1, ă2, ā3}.-2 63A. Is in {ã1, ă2, åz} ? How many vectors are in {ã1, a2, dz}?B. Is 6 in W? How many vectors are in W?C. Show that a is in W. [Hint: Row operations are unnecessary.]

given A=10-403-2-263 , b→=41-4 (a) is b→ in a1→,a2→,a3→?how many vectors are in a1→,a2→,a3→ let…

Answered: 1 -4 Let A 3 -2 and 6 Denote the…

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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1 0 -4
3 -2| and 6
Let A
Denote the columns of A by d1, å2, åz , and let W = Span{ă1, ă2, ā3}.
-2 6
3
A. Is in {ã1, ă2, åz} ? How many vectors are in {ã1, a2, dz}?
B. Is 6 in W? How many vectors are in W?
C. Show that a is in W. [Hint: Row operations are unnecessary.]

Expert Solution

Step 1

given

$A = [\begin{matrix} 1 & 0 & - 4 \\ 0 & 3 & - 2 \\ - 2 & 6 & 3 \end{matrix}], \vec{b} = [\begin{matrix} 4 \\ 1 \\ - 4 \end{matrix}]$

(a) is $\vec{b} in \{\vec{a_{1}}, \vec{a_{2}}, \vec{a_{3}}\}$ ?how many vectors are in $\{\vec{a_{1}}, \vec{a_{2}}, \vec{a_{3}}\}$

let

$\vec{a_{1}} = [\begin{matrix} 1 \\ 0 \\ - 2 \end{matrix}] \vec{a_{2}} = [\begin{matrix} 0 \\ 3 \\ 6 \end{matrix}] \vec{a_{3}} = [\begin{matrix} - 4 \\ - 2 \\ 3 \end{matrix}]$

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