Hello, The solution to problem 6a on page 82 (Advanced EngineeringMathematics, 2

Question

Hello,

The solution to problem 6a on page 82 (Advanced EngineeringMathematics, 2nd Edition, Greenberg) states that "A set of 2functions (u1, u2) is linearly dependent by definition if at leastone of them can be expressed as a linear combination of theothers. u1 = lambda(u2) or u2 = lambda'(u1) for some scalarslambda and lambda'. One is expressible as a scalar multipleof the other."

My question is.....is lambda' an actual derivative of lambda ordoes the prime just indicate that lambda' is another constantcoefficient that is different from lambda??

The "u1 = lambda(u2) or u2 = lambda'(u1) for some scalars lambdaand lambda' " statement in the solution is not shown anywhere inthe description of the theorem (3.2.4) on p. 80 of the text. So, how was i supposed to know this information for the proof ofthe theorem??

Thank you.

Explanation / Answer

Question Details: Hello, ONCE AGAIN LET ME INFORM YOU THAT YOU HAVE TO TYPE THE COMPLETE QUESTION TO GET RESPONSE. AS PER CRAMSTER POLICY CLEARLY OUT LINED, YOU CAN NOT REFER TO TEXTBOOKS ETC.. AND THE QUESTIONS SHALL BE SELF CONTAINED. HOWEVER I AM GIVING MY COMMENTS BELOW BASED ON ASSUMPTIONS... The solution to problem 6a on page 82 (Advanced EngineeringMathematics, 2nd Edition, Greenberg) states that "A set of 2functions (u1, u2) is linearly dependent by definition if at leastone of them can be expressed as a linear combination of theothers. u1 = lambda(u2) or u2 = lambda'(u1) for some scalarslambda and lambda'. One is expressible as a scalar multipleof the other." My question is.....is lambda' an actual derivative of lambda ordoes the prime just indicate that lambda' is another constantcoefficient that is different from lambda?? NO , ' IN THE CONTEXT YOU MENTIONED ARE JUST 2DIFFERENT SCALAR CONSTANTS AND NOT A FUNCTION AND ITSDERIVATIVE.....THAT IS ' IS JUST ANOTHER SCALAR AND NOT ADERIVATIVE OF The "u1 = lambda(u2) or u2 = lambda'(u1) for some scalars lambdaand lambda' " statement in the solution is not shown anywhere inthe description of the theorem (3.2.4) on p. 80 of the text. So, how was i supposed to know this information for the proof ofthe theorem?? NORMAL RECOMMENDED PROCEDURE IS TO WRITE C1U1+C2U2=0 AND CHECK WHETHER THIS IMPLIES C1-C2=0 OR NOT IF YES THEY AREL.I IF NOT THEY ARE L.D. THAT IS A BETTER WAY PARTICULARLY IF THERE ARE MORE THAN 2 VECTORSOR FUNCTIONS Thank you.

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