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An exam for Math 308 H course taken in Autumn 2013 at the University of Washington. The exam consists of a cover sheet and 6 problems related to linear algebra. The exam instructions include an honor statement, time limit, and rules for calculator and notes usage. The problems require showing all work and justifying answers. The exam covers topics such as echelon form, column space, row space, null space, and basis for vector spaces.
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Uploaded on 05/11/2023
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Exam II Autumn 2013
Name Student ID #
“I affirm that my work upholds the highest standards of honesty and academic integrity at the University of Washington, and that I have neither given nor received any unauthorized assistance on this exam.”
SIGNATURE:
GOOD LUCK!
(a) If B is an echelon form of a matrix A, then the pivot columns of B form a basis for the column space of A. ANSWER: (circle one) T F
(b) The column space of a matrix A is equal to the row space of AT^. ANSWER: (circle one) T F
(c) The range of a linear transformation T must contain infinitely many elements. ANSWER: (circle one) T F
(d) If T : Rm^ → Rn^ is a linear transformation, then ker(T ) is a subspace of Rn. ANSWER: (circle one) T F
(e)
(^) is in the null space of the matrix
ANSWER: (circle one) T F
(a) a 3 × 3 matrix A such that row(A) = col(A)
(b) a singular 2 × 2 matrix with no zero entries
(c) a matrix A whose inverse is
(d) a linear transformation T such that T
and T (x) = Ax, where A
is a matrix with no zero entries
(a) Compute rank(A) and nullity(A).
(b) Give a basis for the row space of A.
(c) Give a basis for the null space of A.