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Matrix System -8 -11 -2 x' = 2 X; X1 = e-2t -2 -6 -6 X2 = et -1 X3 = e3t -1

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.5: Determinants

Problem 71E: Explain how to find the determinant of a 22 matrix.

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Question

First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system. find a particular solution of the indicatedlinear system that satisfies the below initial conditions

x₁(0) = 5 , x₂ (0) = -7, x₃ (0)= 11

Matrix System
-8
-11
-2
x' =
2
X; X1 = e-2t
-2
-6
-6
X2 = et
-1
X3 = e3t
-1

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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