# Worksheet: Matrix Differentiation

In this worksheet, we will practice finding the matrix of the linear transformation represented by the differential operator.

Q1:

Consider the vector space of polynomials of degree three at most. The differentiation operator is a linear transformation on this vector space. Find the matrix that represents the linear transformation with respect to the basis .

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Q2:

Consider the vector space of polynomials of degree three at most. The differentiation operator is a linear transformation on this vector space. Find the matrix that represents the linear transformation with respect to the basis .

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Q3:

Consider the vector space of infinitely differentiable functions. The differentiation operator is a linear transformation on this vector space. Find the general form of an element of the kernel of the linear transformation .

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Q4:

Consider the vector space of infinitely differentiable functions. The differentiation operator is a linear transformation on this vector space. Find the general form of an element of the kernel of the linear transformation .

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Q5:

Apply the linear differential operator to evaluate the following expression: .

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