In this exercise you are allowed/encouraged to use the capabilities of matlab in solving the overdetermined equation systems.
The following definitions are useful:
Is1 = [2.7731 2.5720 2.3936 2.2354 2.0952]' Is2 = [1.1921 1.1843 1.1765 1.1688 1.1611]' Is3 = [1.9843 1.9686 1.9532 1.9378 1.9225]' Ir1 = [3.1444 2.4718 1.9431 1.5274 1.2007]' Ir2 = [9.2404 8.5385 7.8899 7.2906 6.7368]' Ir3 = [7.9903 7.9807 7.9710 7.9614 7.9518]' ------------------------------- > could someone please tell me in plain english what we're supposed to be > calculating in q1? > > what are the variables a1, a2, and a3 supposed to represent? The (linear) coefficients indicating the proportions of Ir1,..,3 in the radioactive material found on a particular suspect. > > what do we use the formula of I(t) = Io * exp(l*t) for? This is the (parameterized) mathematical model for the radioactive decay over time (t) for a single radioactive material (isotope) from one of the sources. > > are the 3 pics at the bottom the "victims"? what's their significance? No, they are the (potential) sources of the radioactive materials. --------------- > I don't understand the meaning of question 1 very much and wish to > get some help from you. > 1. Three suspects carry radioactive substance, and three leaders > have radioactive substance, what is the relationship between > suspects and > leaders? Leader can give radioactive substance to suspect? should I > use all data (6 people's) to calculate Io and L according to formula > I(t)=Io*exp(L*t)? > 2. After I get Io and L, how should I calculate a1, a2 and a3? Is > our task to get a1, a2 and a3? In formula Is=a1*Ir1+a2*Ir2+a3*Ir3, > what are Is, Ir1, Ir2 and Ir3 suppose to be? > I think the purpose of this question is to understand how to > calculate solution for a least square problem, but the question > itself really confuses me. Let me expand the question's statement and rewrite the equations. There are three references (sources) of radioactive material (r1, r2, r3). Each reference has its own decay equation Ir1(t) = Ior1 * exp(lr1*t) Ir2(t) = Ior2 * exp(lr2*t) Ir3(t) = Ior3 * exp(lr3*t) There are three suspects (s1, s2, s3) carrying a mix of material from the three references Is1(t) = as1*Ir1(t) + bs1*Ir2(t) + cs1*Ir3(t) Is2(t) = as2*Ir1(t) + bs2*Ir2(t) + cs2*Ir3(t) Is3(t) = as3*Ir1(t) + bs3*Ir2(t) + cs3*Ir3(t) For each suspect, find the contribution of each reference. That is, find the amount of material that s1 carries from r1, r2 and r3. Do the same for s2 and s3.