**Question 6: Explain why S is not a basis for M2x2.****Given Set:**\[ S = \left\{ \begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} \right\} \]**Explanation:**To determine if the set $ S $ is a basis for $ M2x2 $, which is the space of 2x2 matrices, we need to check if $ S $ satisfies two conditions:1. **Spans $ M2x2 $:** A basis must span the entire space of 2x2 matrices. This means any 2x2 matrix should be expressible as a linear combination of the matrices in $ S $.2. **Linear Independence:** The matrices in $ S $ must be linearly independent, meaning no matrix in the set can be written as a linear combination of the others.Since $ M2x2 $ is a 4-dimensional space (as it consists of 2x2 matrices, totaling 4 elements), a basis for this space must contain 4 linearly independent matrices. However, set $ S $ only contains 2 matrices.Therefore, $ S $ cannot be a basis for $ M2x2 $ because it contains fewer matrices than the dimension of the space.

We have t.o show that why S is not Basis for M2,2: Concept: The dimension of a vector space V, is…

Answered: Explain why S is not a basis for M22

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Explain why S is not a basis for M22

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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