# For which values of d are the following sets of

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5. For which value(s) ofdare the following sets of vectors linearly de-pendent? Justify your answers.(a){(1,-1,4)),(3,-5,5),(-1,5, d)}(b){(3,7,-2),(-6, d,4),(9,1,-4)}
(b) Linearly dependent if and only ifd=-14 as-24-41-200d+ 140001.6. Determine, with reasons, whether the following statements are (A)always true, (B) always false, or (C) might be true or false.(a) Ifv1, ...,v5R5andv1=v2+v3, then the set{v1, . . . ,v5}islinearly dependent.(b) Ifv1andv2R2lie on the same straight line through the origin,then the set{v1,v2}is linearly dependent.(c) If{v1,v2,v3}is linearly dependent, then so is{v1,v2,v3,v4}.(d) If{v1,v2,v3}is linearly dependent, then so is{v1,v2}.(e) If{v1,v2}is linearly independent, then so is{v1+v2,v1-v2}.(f) There is a set{v1, . . . ,v5}of linearly independent vectors inR4.
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CalculusRules for Differentiation7. Findf0(x) if
Solution:
8. Suppose thatf(2) = 1,g(2) = 2,f0(2) = 3 andg0(2) = 4. FindF0(2)if
Solution:
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9. A mass on a string of length 0.9m is whirled around in a circle at arate of one revolution every 3.1 seconds.The position (x, y) of themass can be written asx=rcosωt,y=rsinωt.Find the values ofrandωCalculate the speed of the mass (as distance travelled divided bythe elapsed time). Show that this is equal tosdxdt2+dydt2.
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