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Material Type: Exam; Class: Linear Algebra; Subject: Mathematics; University: Arizona State University - Tempe; Term: Spring 2004;
Typology: Exams
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EXAM 1 2
equations is given. Find all solutions to the original system.
(a)
(b)
(c)
(d)
EXAM 1 4
(a) A =
(b) B =
a 0 x
(c) C =
MAT 342 E 5
(a) T F For some n × n matrices A and B, AB = BA.
(b) T F For every matrix A, det(A + A) = det(A) + det(A).
(c) T F For every two invertible n × n matrices A and B, the product AB is invertible.
(d) T F For every invertible matrix A, every matrix which is row-equivalent to A is also
invertible.
MAT 342 E 7
AB = I must be invertible. Hint: Use properties of determinants.
NAME:
12 February 2004
Instructions. You have until 2:55pm to complete this exam.
Be sure to read and follow the instructions for each problem. Be sure to understand each
problem carefully before starting work on it. Be sure to show your work and clearly indicate
your final answers.
No notes, books, or calculators are allowed.
Problem Points Score
Total 100
S. Kaliszewski, Department of Mathematics and Statistics, Arizona State University