Advanced Engineering Mathematics
Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 10, Problem 1CR
To determine

The blank in the statement: “The vector X=k(45) is a solution of X=(1421)X(81) for k=_________________.”

Expert Solution & Answer
Check Mark

Answer to Problem 1CR

The vector X=k(45) is a solution of X=(1421)X(81) for k=13_.

Explanation of Solution

Given:

The systems of differential equation is X=(1421)X(81).

Calculation:

The vector is X=k(45) and the differentiation is X=(00) as the given vector is constant.

Substitute k(45) for X and (00) for X for in equation X=(1421)X(81).

X=(1421)k(45)(81)(00)=(1421)(4k5k)(81)(00)=(1(4k)+4(5k)2(4k)1(5k))(81)(00)=(4k+20k8k5k)(81)

Further simplify the above equation.

(00)=(24k3k)(81)(00)=(24k83k1)

From above equation, 3k1=0 so the value of k is calculated as follows:

3k1=03k=1k=13

Therefore, the value of k is 13.

Thus, the vector X=k(45) is a solution of X=(1421)X(81) for k=13_.

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Chapter 10 Solutions

Advanced Engineering Mathematics

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