4. Consider the subspace spanned by B = {cos(x), sin(x), x cos(x), x sin(x)} inside thespace of continuous functions. B is in fact a basis for its span. The derivative is alinear transformation on this span, and it acts as follows:D(cos(x)) = – sin(x)D(sin(x)) = cos(x)D(x cos(x)) = cos(x) – x sin(x)D(x sin(x)) = sin(x) + x cos(x)Find the matrix representing D in this basis. Use this to computeD(3 cos(x) – 2 sin(x)+x cos(x) – 2.x sin(x))without computing any derivatives. (show the matrix and column vector you use todo this, and the resulting column vector before converting back to functions)

Name: 4. Consider the subspace spanned by B = {cos(x), sin(x), x cos(x), x
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Description: 4. Consider the subspace spanned by B = {cos(x), sin(x), x cos(x), x sin(x)} inside thespace of continuous functions. B is in fact a basis for its span. The derivative is alinear transformation on this span, and it acts as follows:D(cos(x)) = – sin(

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Consider the subspace spanned by B = {cos(x), sin(x), x cos(x), x sin(x)} inside the space of continuous functions. B is in fact a basis for its span. The derivative is a linear transformation on this span, and it acts as follows: D(cos(x)) = – sin(x) D(sin(x)) = cos(x) D(x cos(x)) = cos(x) – x sin(x) D(r sin(x)) = sin(x) + x cos(x) Find the matrix representing D in this basis. Use this to compute D(3 cos(x) – 2 sin(x) + x cos(x) – 2x sin(x)) without computing any derivatives. (show the matrix and column vector you use to do this, and the resulting column vector before converting back to functions)

Consider the subspace spanned by B = {cos(x), sin(x), x cos(x), x sin(x)} inside the space of continuous functions. B is in fact a basis for its span. The derivative is a linear transformation on this span, and it acts as follows: D(cos(x)) = – sin(x) D(sin(x)) = cos(x) D(x cos(x)) = cos(x) – x sin(x) D(r sin(x)) = sin(x) + x cos(x) Find the matrix representing D in this basis. Use this to compute D(3 cos(x) – 2 sin(x) + x cos(x) – 2x sin(x)) without computing any derivatives. (show the matrix and column vector you use to do this, and the resulting column vector before converting back to functions)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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