For each set below

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Linear algebra and vector spaces · Linear algebra and vector spaces

Mathematical Methods for Physics, Ch Vector spaces, bases, linear maps and dual vectors

Problem

For each set below, decide whether it is linearly independent, and state the dimension of the space it spans. ((a)) The functions

e^{-t}

and

te^{-t}

, the two solutions of the critically damped equation

\ddot x + 2\dot x + x = 0

in the form Chapter 8 gave. Use the Wronskian of Chapter 9. ((b)) The three functions

1

\cos^2 t

and

\cos 2t

. ((c)) The three columns

(1,2,0)

(0,1,1)

and

(2,3,1)

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