Question

• —————— The polynomials of degree less than 5 form a 5-dimensional subspace of the vector space of all polynomials. • —————— If W is a subspace of V, and if W is finite dimensional, then V must be finite dimensional as well. • —————— If f1,...,fn are polynomials such that deg fi = i for i = 1,...,n, then f1,...,fn must be linearly independent. • —————— Let P be the space of polynomials with real coefficients and T : P ? ? the linear map given by T(f(t)) = ??¹ f(t)dt The kernel of T is finite dimensional. • —————— The function T : P5 ? P5 given by T(f(t)) = d/dt ??³??? f(x)dx is an isomorphism. • —————— Any 4-dimensional vector space has infinitely many 3-dimensional subspaces. • —————— The identity matrix In is similar to all invertible n x n matrices. • —————— Matrix In is similar to the matrix 2In. • —————— All invertible matrices are diagonalizable. • —————— If two matrices have the same characteristic polynomials, then they must be similar.

          • —————— The polynomials of degree less than 5 form a 5-dimensional subspace of the vector space of all polynomials.
• —————— If W is a subspace of V, and if W is finite dimensional, then V must be finite dimensional as well.
• —————— If f1,...,fn are polynomials such that deg fi = i for i = 1,...,n, then f1,...,fn must be linearly independent.
• —————— Let P be the space of polynomials with real coefficients and T : P ? ? the linear map given by
T(f(t)) = ??¹ f(t)dt
The kernel of T is finite dimensional.
• —————— The function T : P5 ? P5 given by
T(f(t)) = d/dt ??³??? f(x)dx
is an isomorphism.
• —————— Any 4-dimensional vector space has infinitely many 3-dimensional subspaces.
• —————— The identity matrix In is similar to all invertible n x n matrices.
• —————— Matrix In is similar to the matrix 2In.
• —————— All invertible matrices are diagonalizable.
• —————— If two matrices have the same characteristic polynomials, then they must be similar.

• —————— The polynomials of degree less than 5 form a 5-dimensional subspace of the vector space of all polynomials.
• —————— If W is a subspace of V, and if W is finite dimensional, then V must be finite dimensional as well.
• —————— If f1,...,fn are polynomials such that deg fi = i for i = 1,...,n, then f1,...,fn must be linearly independent.
• —————— Let P be the space of polynomials with real coefficients and T : P ? ? the linear map given by
T(f(t)) = ??¹ f(t)dt
The kernel of T is finite dimensional.
• —————— The function T : P5 ? P5 given by
T(f(t)) = d/dt ??³??? f(x)dx
is an isomorphism.
• —————— Any 4-dimensional vector space has infinitely many 3-dimensional subspaces.
• —————— The identity matrix In is similar to all invertible n x n matrices.
• —————— Matrix In is similar to the matrix 2In.
• —————— All invertible matrices are diagonalizable.
• —————— If two matrices have the same characteristic polynomials, then they must be similar.

Added by Russell F.

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