2×2(a) The set of all 2 × 2 symmetric matrices is a subspace of R²x2. Find a basis for thissubspace, and find the coordinates of-1in that basis.(b) The set of all 2 x 2 upper-triangular matrices is a subspace of R-*2. Find a basis for thissubspace, and find the coordinates of-3-21in that basis.2×2(c) Is the set of 2 × 2 matrices that are symmetric and upper-triangular a subspace of IR²*²?Why or why not?2×2(d) Is the set of 2 × 2 matrices that are symmetric or upper-triangular a subspace of IR'? Whyor why not?

We need to find the basis for 2×2 symmetric matrices and upper triangular matrices. Also we need to…

Answered: (a) The set of all 2 × 2 symmetric…

(a) The set of all 2 × 2 symmetric matrices is a subspace of R²×². Find a basis for this subspace, and find the coordinates of -1 in that basis.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 16AEXP

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

2×2
(a) The set of all 2 × 2 symmetric matrices is a subspace of R²x2. Find a basis for this
subspace, and find the coordinates of
-1
in that basis.
(b) The set of all 2 x 2 upper-triangular matrices is a subspace of R-*2. Find a basis for this
subspace, and find the coordinates of
-3
-2
1
in that basis.
2×2
(c) Is the set of 2 × 2 matrices that are symmetric and upper-triangular a subspace of IR²*²?
Why or why not?
2×2
(d) Is the set of 2 × 2 matrices that are symmetric or upper-triangular a subspace of IR
'? Why
or why not?

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