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 .

• A
• B
• C
• D
• E

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 .

• A
• 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 .

• A
• B
• C
• D
• E

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 .

• A
• B
• C
• D
• E