Mathematics 1229A/B Lecture 3: September 12 Notes
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MATH 1229A/B Full Course Notes
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= (1+1, 0+0: start at origin (0,0) by the number c. Could also consider i. e. (2,0) = (1,0) + (1,0) On (cid:2870) plane: travel along (cid:2835) , travel along (cid:1827)(cid:1828) (translation of (cid:2835) ) to (1,0) For any vector (cid:1873) and any scalar c, the vector (cid:1855)(cid:1873) is obtained by multiplying each component of (cid:1873) . In (cid:2870), (cid:1855)(cid:1873) = c((cid:1873)(cid:2869), (cid:1873)(cid:2870)) = ((cid:1855)(cid:1873)(cid:2869), (cid:1855)(cid:1873)(cid:2870)) In (cid:2871), (cid:1855)(cid:1873) = c((cid:1873)(cid:2869), (cid:1873)(cid:2870), (cid:1873)(cid:2871)) = ((cid:1855)(cid:1873)(cid:2869), (cid:1855)(cid:1873)(cid:2870), c(cid:1873)(cid:2871)) In (cid:2871) = (cid:1873) + (cid:1874) = ((cid:1873)(cid:2869) + (cid:1874)(cid:2869), (cid:1873)(cid:2870) + (cid:1874)(cid:2870), (cid:1873)(cid:2871) + (cid:1874)(cid:2871)) Find a(cid:2835) + b(cid:2836) + c where a, b, c are scalars a(cid:2835) + b(cid:2836) + c = a(1, 0, 0) + b(0,1, 0) + c(0, 0, 1) In (cid:2870) (cid:1873) = ((cid:1873)(cid:2869), (cid:1873)(cid:2870)) = (cid:1873)(cid:2869)(cid:2835) + (cid:1873)(cid:2870)(cid:2836) . In (cid:2871) (cid:1873) = ((cid:1873)(cid:2869), (cid:1873)(cid:2870),(cid:1873)(cid:2871)) = (cid:1873)(cid:2869)(cid:2835) + (cid:1873)(cid:2870)(cid:2836) + (cid:1873)(cid:2871) .