Let A -[88] QUESTION 1 and consider the following subspaces of M2x2 (C) defined by W₁ = {X € M2x2 (C): AX=-X} and W₂ = {X € M2x2 (C): AX = XA} (1.1) Find a basis for W₁. (1.2) Find a basis for W₁ W₂.

Let A -[88] QUESTION 1 and consider the following subspaces of M2x2 (C) defined by W₁ = {X € M2x2 (C): AX=-X} and W₂ = {X € M2x2 (C): AX = XA} (1.1) Find a basis for W₁. (1.2) Find a basis for W₁ W₂.

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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Expert Solution

Step 1

Given two subspaces $W_{1}, W_{2}$ of a vector space $M_{2 x 2} (C)$ ( set of all 2x2 matrices over the field of complex numbers ) defined by ,

$W_{1} = \{X \in M_{2 x 2} (C) : A X = - X\}$ $,$ $W_{2} = \{X \in M_{2 x 2} (C) : A X = X A\}$

and $A = [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]$

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