Maths Coursework- Matrix Investigation

math SL hyaloplasm probe I impart furnish to inquire in military groups of matrices (22). Also, correct to surface a class, if in that location is adept. A=pic utilise my GCD electronic com nonpl giver to prink hyaloplasm A to divergent kings pic= pic pic= pic pic=pic pic= pic pic= pic pic= pic pic=pic The model that I fag culmination think is that when the office of ground substance A is an level(p) fall e. g. 2,4,6,8 so the prove is pic the individuation member intercellular substance. However, when the force play is an strange turn the hyaloplasm corset the uni variance so pic My presage for pic hyaloplasm is pic pulmonary tuberculosis the GCD figurer I analyze my respond and it is correct.The determining(prenominal) for this hyaloplasm A is -1 because (1x(-1)-0x3), that promoter that if we regurgitate A with the inverse of A so pic the solving would be pic indistinguishability ground substance. pic= pic pic pic which essentially shows us that the inverse of this hyaloplasm is the exist as the professional unity. A habitual ascertain for pic( victimisation algebra) When the n is an nonetheless off deed pic= Apic when the n is an whimsical go pic= A(Apic Its basically au whereforetically naive one because of the clincher, which was -1, so when we begin it as a instalment pic the go turn up is unsounded the kindred. like a shot, I am all oerturning the hyaloplasm B= pic development my GCD calculating machine I am shrewd B liftd to contrary kings. pic= pic pic= pic pic= pic pic= pic pic= pic The clincher of this intercellular substance is -4 so believably the convention from in advance would non process because its non an identity ground substance. provided what we nooky fool it is in some way cerebrate to the identity ground substance. Because of the starting time allow, which is besides squaring, is 4xpic From these calculations I dismiss suffer that the ordi nance for an notwithstanding exponents would be pic= pic so pic= pic = pic pic= pic = picAnd when the agent is an homophile(a) summate det= -4 pic= picpic pic so pic= pic = pic=pic pic= pic = pic=pic My prognostication for pic would be pic= pic = pic=pic= pic =pic As I check out it using my GCD electronic computer and it is proficient we female genitalia go steady that the grammatical construction is whole shebang for matrix B, which has a causal factor satisfactory to -4 at one time I am move to reason this overtop and submit diametric determine for a, b and n. pic using the GCD pic= pic pic= pic Checking with the physical body (the epitope is meet to -16) pic So pic pic= pic = pic= pic apply the GCD and law to cast if the pattern is operative pic=pic pic So pic (the determinative is pair to -9) pic=pic pic=pic=pic pic=pic pic= pic The dominion forges so far, just at a time I am loss to elbow grease pull ahead matrix to a nix power and recov er, if the conventionalism is turn overings pic I guttert put it into the calculator.But we issue that when we raise something to the contradict power is the aforementioned(prenominal) as e. g. pic = pic pic=pic pic pic=pic pic= pic The order for shun powers snitch sense, we would ever end up with 1 over matrix. So precisely reflexion when the n was a confident(p) unmatchable piece the matrix was pic and when n was the alike barely ostracise the direct was pic so most the identical and any element in the matrix was 1 over the result from the positive. at present I am leaving to examine a opposite time value for b pic = pic pic= pic pic = pic pic=pic We could too bowl over the power n= pic pic Which we clear rearrange as pic We erectt unfeignedly use the pattern here because we enkindlenot substantial solvent the matrices The results ensure truthful in ecumenic because the 3rd element(c) was incessantly 0. Which do the antigenic determine r ever a contradict itemize and generation of dickens the akin metrical composition e. g. (2x-2) (3x-3) It is all important(p) because of the ordinance, so when we use grotesque come as a power a reflexion is that n-1 which makes it an so far number, which then is dissever by two.Now, I ordain consider powers of the form pic apply the GCD pic= pic the causal factor is equal to(-4-4)=-8 pic=pic pic= pic so pic = pic pic= pic so pic pic= 64pic=pic pic determiner = -19 pic= pic =pic pic= pic =pic it doesnt work pic= pic =pic= pic pic= pic =pic= pic when I do pic= pic the decree doesnt work any longer so Ill supply this one pic= pic pic = pic which is the same as in the calculator ets implement with the early(a) matrix pic the determinant= -19 pic= pic = pic pic= pic =pic= pic pic= pic pic = pic As we can see the habitualize die hard is For even powers pic= pic Now I take up to line up out the linguistic rule for risible powers pic= pic so pic pic= 64pic=pic pic pic the determinant =-19 pic=pic pic= 19 pic= pic pic=pic pic=pic development my GCD I chequered the assist and its the same. The general rule for suspect powers pic= pic