Leb A,=and let A = I e M2Show thatSpan [A, A] = [ zab :a,be C]-6[:commuting family.Spec Za,b = [atib] with associatedain whichZabExplain%3Dawhyspan [AI, A] isShow thatvectarswhatis%3Deigen-コチ1 ] = キxZeos D, Sin o

The given matrix is A1=0-110 and A2=1001. And Za,b=a-bba: a,b∈ℂ. Therefore the span of A1, A2 can be…

Answered: Let A,= and let A = I e M2 Span [A, A]…

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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Related questions

Question

Leb A,=
and let A = I e M2
Show that
Span [A, A] = [ zab :a,be C]
-6
[:
commuting family.
Spec Za,b = [atib] with associated
a
in which
Zab
Explain
%3D
a
why
span [AI, A] is
Show that
vectars
what
is
%3D
eigen
-コチ1 ] = キx
Zeos D, Sin o

Expert Solution

Step 1

The given matrix is $A_{1} = [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]$ and $A_{2} = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ .

And $\begin{array}{rcl} Z_{a, b} & = & \{[\begin{matrix} a & - b \\ b & a \end{matrix}] : a, b \in ℂ\} \end{array}$ . Therefore the span of $A_{1}, A_{2}$ can be written as:

$\begin{array}{rcl} s p a n [A_{1}, A_{2}] & = & \{a [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] + b [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}] + b [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] : a, b \in ℂ\} \\ = & \{[\begin{matrix} a & - b \\ b & a \end{matrix}] : a, b \in ℂ\} \\ = & Z_{a, b} \end{array}$