Matrix- System of rows and columns each position in a matrix has a purpose. 5 Ex: 5. Ex:

Transcription

1 Mtries Prelulus Mtri- Sstem of rows n olumns eh position in mtri hs purpose. Element- Eh vlue in the mtri mens the element in the n row, r olumn Dimensions- How mn rows b number of olumns Ientif the element: Nme mtries with pitl letters. Row mtri- hs one row Column mtri- hs one olumn Squre mtri- sme # of rows s olumns. Equl mtries- hve the sme imensions n hve orresponing elements. Solve for eh vrible- z ition & Subtrtion- Mtries must hve sme imensions. Move Qu BCD units to the left n units up (-, -), (, -), (, ), (, -). Slr multiplition- multipling b onstnt

2 Enlrge BC with verties (-, ), B(-, -) n C(, -) so tht it s perimeter is twie s lrge s the originl figure. -oorinte: -oorinte: D Homework Nme. Perform the inite opertion, if possible. If not possible stte the reson Solve for n... Use the informtion bout Mjor Legue Bsebll tems wins n losses in before n fter the ll-str Gme. Before: tlnt Brves h wins n losses, Settle Mriners h wins n losses, n Chigo Cubs h wins n losses. fter: Brves h wins n losses, Mriners h wins n losses, n Cubs h wins n losses.. Use mtries to orgnize the informtion.write mtri tht shows the totl number of wins n losses for the tems in.

3 Mtri Multiplition D. = How?. = Let s think bout the imensions first. Your Turn:?

4 Cummuttive Propert Wht hppens when we multipl Prtie:

5 Unit Mtries Nme D Homework Determine the imensions of eh mtri M.. M B. B M. B M Fin the prout of eh, if possible X

6 Determinnt- squre rr of # s or vribles enlose between two prllel vertil brs. Eh # or vrible is lle n element. Mtri: Rows b vlue is b Columns E- E- E- E- Mtri: Move first two olumns over n multipl igonll like. nother w is epnsion b minors, where the minor of n element is the eterminnt forme when the row n olumn ontining tht element is elete. h e g i f g b i f h e i h g f e b Fin the eterminnt of mtri. E- E- Fin the eterminnt of the mtri b using the epnsion of minors. E- E- Remember:

7 Inverse of Squre Mtri: Definition of the Inverse of Squre Mtri Let be n mtri. If there eists mtri suh tht I n Inverse of Mtri: b then b et B B C C D D How o we fin the inverse of? Inverse of Mtri: Mtri Eqution: = + = - = *Orer will mtter with mtries.) Fin the inverse of the oeffiient mtri.) Multipl b the inverse on both sies (*inverse goes first).) nswer is n orere pir.

8 E- Solve the following sstems using mtri eqution:.. z z z re of Tringle: = where the is use to get positive re. E - Fin the re of the tringle E - Fin the re of the tringle (, -) (, ) (, ) (, -) (, ) (, -) = Test for Colliner Points: = = Determine whether (-, -) (, ) (, ) re olliner. Crmer s Rule: + b = e eliminte : eliminte : + = f e bf b f e b Notie: - b = b

9 E- = + = - = = E- = E- + = = = = = E- = E- - + = + = + = Crmer s + z = + z = - + z = z Solve for : Solve for : E- + z = - E- + b = - + z = - + b + = - + z = b =

10 Solve using mtries: E- + + z = E- + = - = b = - + z = + b + = E - + z = E- + = + z = + = - z = - + z = nlsis of Network: In network, it is ssume tht the totl flow into juntion is equl to the totl flow out of the juntion. For instne, juntion one hs units flowing in so + =. Set up sstem of equtions n solve for the unknown vlues. Solve the mtri eqution for X: X