Let \( W \) be the subspace of \( M_{2 \times 2}(\mathbb{R}) \)\[W = \left\{ \begin{bmatrix} 2a + b & 3c + d \\ -d & 0 \end{bmatrix} : a, b, c, d \in \mathbb{R} \right\}.\](a) Find a basis for \( W \). You do not need to prove that it is a basis.(b) \( W \) is isomorphic to \( \mathbb{R}^n \) for some \( n \). Put the value of this \( n \) in this box: \(\Box\)(c) Prove that \( W \) is isomorphic to \( \mathbb{R}^n \), where \( n \) is your value from part (b).

Answered: (a) (b) (c) Let W be the subpace of…

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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(a) (b) (c) Let W be the subpace of M2x2 (R) b W = { [20 + $ 30+d]:akedER} a, b, c, Find a basis for W. You do not need to prove that it is a basis. W is isomorphic to Rn for some n. Put the value of this n in this box: Prove that W is isomorphic to R", where n is your value from part (b).