3. Consider the function || · ||p¹ : R² → R defined as follows: for any x = (x₁, x2) € R², set1||||/³₁ = 3x² + x1x2 + x³².(a) Find a symmetric matrix A € R²X² such that||||²/₁ = x¹ Ax,(b) Show that A above is positive definite(c) Show that ||- ||p¹ : R² → R is a norm.for all x € R².

Consider:·P1:R2→R define as follows: x2P1=13x12+x1x2+x22 To Find: a) Symmetric matrix A such that…

3. Consider the function || ||p₁ : R² → R defined as follows: for any x = (1, ₂) = R², set 1 = 3x² + x1x₂ + x². 2². ||||²³₁= (a) Find a symmetric matrix A € R²x2 such that ||||²/₁ x¹ Ax, = (b) Show that A above is positive definite (c) Show that ||- ||p₁: R² → R is a norm. for all x € R².

3. Consider the function || ||p₁ : R² → R defined as follows: for any x = (1, ₂) = R², set 1 = 3x² + x1x₂ + x². 2². ||||²³₁= (a) Find a symmetric matrix A € R²x2 such that ||||²/₁ x¹ Ax, = (b) Show that A above is positive definite (c) Show that ||- ||p₁: R² → R is a norm. for all x € R².

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 3EQ: In Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB,...

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