Chapter 4.7, Problem 25E

(a)

To determine

Whether the statement “If $y_1\text{ and }{y}_2$ are linearly dependent on the interval $\left[a,b\right]$, then $y_1\text{ and }{y}_2$ are linearly dependent on the smaller interval $\left[c,d\right]\subset \left[a,b\right]$” is true or false.

(b)

To determine

Whether the statement “If $y_1\text{ and }{y}_2$ are linearly dependent on the interval $\left[a,b\right]$, then $y_1\text{ and }{y}_2$ are linearly dependent on the larger interval $\left[C,D\right]\supset \left[a,b\right]$” is true or false.