MAT 342 E 1
1. (15) Find all solutions to the following system of linear equations. Show your work.
x+ 3y−z+w= 8
x+ 3y+z−w= 2
−2z+ 3w=−4
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Questions of Linear Algebra - Exam 1 | MAT 342, Exams of Linear Algebra
Material Type: Exam; Class: Linear Algebra; Subject: Mathematics; University: Arizona State University - Tempe; Term: Spring 2004;
Typology: Exams
Pre 2010
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1. (15) Find all solutions to the following system of linear equations. Show your work.
- MAT 342 E
- x + 3y − z + w =
- x + 3y + z − w = - − 2 z + 3w = −
EXAM 1 2
- (16) In each part, the reduced echelon form of the augmented matrix of a system of linear
equations is given. Find all solutions to the original system.
(a)
(b)
(c)
(d)
EXAM 1 4
- (12) Find the determinant of each matrix:
(a) A =
(b) B =
a 0 x
(c) C =
MAT 342 E 5
- (16) True or False? Circle T or F and give a brief justification of your answer.
(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
- (10) Prove that every n × n matrix A for which there exists an n × n matrix B such that
AB = I must be invertible. Hint: Use properties of determinants.
NAME:
MAT 342 E
EXAM 1
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