Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. For each of the following statements, determine if the conclusion ALWAYS follows from the assumptions, if the conclusion is SOMETIMES true given the assumptions, or if the conclusion is NEVER true given the assumptions. You do not need to show any work or justify your answers to these questions - only your circled answer will be graded. (a) If A and B are matrices and AB = 0 (the zero matrix), then A=0 or B = 0. ALWAYS SOMETIMES (b) If X(t) is a solution to the linear system X'= AX, then et X(t) is also a solution. ALWAYS SOMETIMES NEVER NEVER (c) If a 2 x 2 matrix A has real distinct eigenvalues and det A = 1, then 0 < trace(A) < 2. ALWAYS SOMETIMES NEVER

1. For each of the following statements, determine if the conclusion ALWAYS follows from the assumptions, if the conclusion is SOMETIMES true given the assumptions, or if the conclusion is NEVER true given the assumptions. You do not need to show any work or justify your answers to these questions - only your circled answer will be graded. (a) If A and B are matrices and AB = 0 (the zero matrix), then A=0 or B = 0. ALWAYS SOMETIMES (b) If X(t) is a solution to the linear system X'= AX, then et X(t) is also a solution. ALWAYS SOMETIMES NEVER NEVER (c) If a 2 x 2 matrix A has real distinct eigenvalues and det A = 1, then 0 < trace(A) < 2. ALWAYS SOMETIMES NEVER

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 40E
See similar textbooks
icon
Related questions
Question
1. For each of the following statements, determine if the conclusion ALWAYS follows from the assumptions, if the conclusion is SOMETIMES true given the assumptions, or if the conclusion is NEVER true given the assumptions. You do not need to show any work or justify your answers to these questions - only your circled answer will be graded. (a) If A and B are matrices and AB = 0 (the zero matrix), then A = 0 or B = 0. SOMETIMES ALWAYS (b) If X(t) is a solution to the linear system X'= AX, then etX(t) is also a solution. ALWAYS ALWAYS SOMETIMES (c) If a 2 x 2 matrix A has real distinct eigenvalues and det A = 1, then 0 < trace(A) < 2. SOMETIMES ALWAYS NEVER SOMETIMES NEVER (d) If det A = 0, then the system X' = AX has more than two equilibrium solutions. ALWAYS NEVER SOMETIMES NEVER (e) If M = [2] and X(t) is a solution to the planar linear system X' = AX, then Y (t) = MX(t) is also a solution to the system X' = AX. NEVER
Transcribed Image Text:1. For each of the following statements, determine if the conclusion ALWAYS follows from the assumptions, if the conclusion is SOMETIMES true given the assumptions, or if the conclusion is NEVER true given the assumptions. You do not need to show any work or justify your answers to these questions - only your circled answer will be graded. (a) If A and B are matrices and AB = 0 (the zero matrix), then A = 0 or B = 0. SOMETIMES ALWAYS (b) If X(t) is a solution to the linear system X'= AX, then etX(t) is also a solution. ALWAYS ALWAYS SOMETIMES (c) If a 2 x 2 matrix A has real distinct eigenvalues and det A = 1, then 0 < trace(A) < 2. SOMETIMES ALWAYS NEVER SOMETIMES NEVER (d) If det A = 0, then the system X' = AX has more than two equilibrium solutions. ALWAYS NEVER SOMETIMES NEVER (e) If M = [2] and X(t) is a solution to the planar linear system X' = AX, then Y (t) = MX(t) is also a solution to the system X' = AX. NEVER
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS