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The second midterm exam for math 232, held in spring 2007. The exam covers various topics in linear algebra, including determinants, matrices, subspaces, and bases. Students are required to compute determinants, find bases for null spaces and column spaces, and prove that certain sets are subspaces.
Typology: Exams
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(a) (3 points) Find a basis for Nul(A)
Answer
(b) (3 points) Find a basis for Col(A)
Answer
(c) (1 point) What is the rank of A?
Answer
(b) (3 points) Prove that H is a subspace of P 3.
Answer
(c) (3 points) Give a basis of H. Explain why your answer is correct.
(c) (3 points) Let c 1 =
(^) , c 2 =
. Compute [c 1 ]B and [c 2 ]B.
Answer
(d) (2 points) Let C = {c 1 , c 2 }. Compute PB←C.