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Worksheet: 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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  • B
  • C
  • D
  • E

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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  • B
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  • D
  • E