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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

Uploaded on 09/02/2009

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MAT 342 E 1
1. (15) Find all solutions to the following system of linear equations. Show your work.
x+ 3yz+w= 8
x+ 3y+zw= 2
2z+ 3w=4
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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

  1. (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

  1. (12) Find the determinant of each matrix:

(a) A =

(b) B =

a 0 x

(c) C =

MAT 342 E 5

  1. (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

  1. (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