Reference no: EM131076214
MATH 54 QUIZ 4-
1. Let P4 be the vector space of polynomials of degree at most 4, and let V be the subset of polynomials of degree exactly 4. Is V a subspace of P4? Explain your reasoning.
2. Let M2×2 be the vector space of 2 × 2 matrices. Let H be the subset of M2×2 consisting of matrices A such that det A = 0. Is H a subspace of M2×2? Explain your reasoning.
3. Find the coordinates of 
relative to the basis B = 
of R3.
4. Let P2 be the vector space of polynomials of degree at most 2. It is given that B = {1 + t, t + t2, 1 + t2} is a basis for P2. Find the coordinates of t2 relative to B.
5. Suppose that T : V → W is an injective (one-to-one) linear transformation. Let {v1, . . . , vn} be a linearly independent set in V . Prove that {T(v1), . . . , T(vn)} linearly independent.
6. Let V = {(a1, a2, . . .) : ai ∈ R} be the vector space of infinite sequences of real numbers. The right shift operator is a linear transformation T : V → V defined by T((a1, a2, . . .)) = (0, a1, a2, . . .). Find the kernel and range of T.
7. Write anything you like here (comments, questions, suggestions, etc).
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