**Problem 1**: Find a basis **and determine the dimension** of the following sub-spaces.\[ H = \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \Big| \ a - c = 0 \right\} \]This problem involves identifying a basis and determining the dimensionality of a subspace described by matrices with a specific condition, in this case, where the elements \( a \) and \( c \) are equal.

We have to find the basis and dimension of subspace

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1: Find a basis and determine the dimension of the following sub-spaces. H = { : 1a-c=0}. a b {: la-c=0}. d

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Problem 1**: Find a basis **and determine the dimension** of the following sub-spaces.

\[ H = \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \Big| \ a - c = 0 \right\} \]

This problem involves identifying a basis and determining the dimensionality of a subspace described by matrices with a specific condition, in this case, where the elements \( a \) and \( c \) are equal.

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