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X' = AX has a saddle. ALWAYS where D = det A and I ALWAYS SOMETIMES ace(A), and A is a 2 x 2 matrix, then the system (e) If x(t) and y(t) are solutions to the equation x" + px' + qx = sint and x'(0) = y'(0), then x(t)= y(t), for all t. SOMETIMES NEVER NEVER

X' = AX has a saddle. ALWAYS where D = det A and I ALWAYS SOMETIMES ace(A), and A is a 2 x 2 matrix, then the system (e) If x(t) and y(t) are solutions to the equation x" + px' + qx = sint and x'(0) = y'(0), then x(t)= y(t), for all t. SOMETIMES NEVER NEVER

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3BEXP
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(d) If D = T²+1, where D = det A and T = trace(A), and A is a 2 × 2 matrix, then the system X' = = AX has a saddle. ALWAYS SOMETIMES ALWAYS (e) If x(t) and y(t) are solutions to the equation x" + px' + qx = sint and x'(0) = y'(0), then x(t) = y(t), for all t. NEVER SOMETIMES NEVER
Transcribed Image Text:(d) If D = T²+1, where D = det A and T = trace(A), and A is a 2 × 2 matrix, then the system X' = = AX has a saddle. ALWAYS SOMETIMES ALWAYS (e) If x(t) and y(t) are solutions to the equation x" + px' + qx = sint and x'(0) = y'(0), then x(t) = y(t), for all t. NEVER 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. (a) If X(t) is a non-zero solution to the linear system X' = AX, where A is a 2 × 2 matrix with det A = 0, and X(1) = X(0), then A has imaginary eigenvalues. ALWAYS ALWAYS (b) If x(t) is a solution to a damped unforced mass-spring oscillator equation, then x(t) → 0, as t→→∞. (c) If X(t) = ALWAYS SOMETIMES [0] SOMETIMES NEVER SOMETIMES NEVER is a solution to the system X' = AX, then x(t)² + y(t)² → ∞, as t → 1. 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. (a) If X(t) is a non-zero solution to the linear system X' = AX, where A is a 2 × 2 matrix with det A = 0, and X(1) = X(0), then A has imaginary eigenvalues. ALWAYS ALWAYS (b) If x(t) is a solution to a damped unforced mass-spring oscillator equation, then x(t) → 0, as t→→∞. (c) If X(t) = ALWAYS SOMETIMES [0] SOMETIMES NEVER SOMETIMES NEVER is a solution to the system X' = AX, then x(t)² + y(t)² → ∞, as t → 1. NEVER
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