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Accelerated Integrated Geometry 10.1 Introduction to Matrices ¢ Matrix: a rectangular array of numbers enclosed ina single set of brackets ¢ Dimensions: the number of horizontal rows and vertical columns in a matrix example: a2 ° | -3 4 «12 row 2x3 a, =O P\ ane column ¢ Examples: Addition and Scalar Multiplication... Let A= 201 and B= 57 4 : 5 -7 8 02 8 1. A+B 2. A-B [-aes o+7 ta (-') “25 0-7 IO) | [540-42 beee) | ~ S-0 -1-2 Be(-8) | 7 f3 7 2] “7-702 ;s -5 Of 5-9 16 0 Oo -10 5 LetA=|4 1landB=|0 4]. 3 = «5 -7 3 3, A+B 4, A-B 0+ (105 o+5 a) 0- (40) ors 10 440 14 =ly os 4-0 \-4 = 4 “10 7-2 -B-(-7) 0-53 4 -3¢(-7) “S43 ; () 5. 4A 6. “FASB 0 0 (a) o _ifo o 10 5] Yiu i feole 4 ase] tis aye -3 5 “1% -20 -10 S -2 4 -2o te Properties of Matrix Addition: For matrices A, 8, and C, each with dimensions of mxn.. Commutative A+B=B+A Associative (A+B)+C=A+(B+C) Additive Identity The men matrix having 0 as all of its entries is the mxn identity matrix for addition. Additive Inverse For every mxn matrix A, the matrix whose entries are the opposite of those in A is the additive inverse of A. Examples: Solve for xand y. 7 25x 3y+5] [-10 2 “L4 oy Fle y 25x2-!10 Byt+S=% 7s x4 “$s -5 c-UV Base yearly oft Ls I> a alee, Ate]: (F] Sara S| -8G =| 3 -p-ay}~ | 3 27 152t+9=-36 . tae 3y ar a “4-4 +12 tz [SH = 4S, r3y = 215 is 15 BB re -3 7 — ye Sw ¢ Examples: Find each product. uel? 3 “1 5 1, Find H6. 2-3 60]. “7 ak i. AL Cold Ry Giz. 2ebi2) — o+¢ri) R2 ColZ R212) = 6420-0435 [7 | ee 3. a Rw. Rw) 2 3x2 2x2 le s| xX [i °]- dng: 3¥2 ipe2) — O+(-21) 0420 0+35 = -l0+0 [o) “2-2 20 35 “10 O 5. Find HW. HW ed [; 2] ah (0) 2 242 1s “uo? = Ww 2, Find GH. OTe oy = 2% 47 15 pe Soret 1240 -184+0 S47 2435 | | size of on answer 12 18 5 2 4, Find WR. WR. voy 2x2 3xZ Do not match YOU. Lonnot multiply Accelerated Integrated Geometry 10.3 Determinant and Inverse of a Matrix « Square Matrix: a matrix with the same number of rows and columns « Identity Matrix: a square matrix with ones down the main diagonal and zeros everywhere else ; ‘1a 0 10 ; I= Ot T=|O.1 0 0 \, sensor 2 > Any matrix multiplied by Ihas a product of the original matrix. main diagonal > Any matrix multiplied by its inverse has a product of I. Let a=|¢ 3] ond B= 5 3) 3.5 302 1. Show that A and Bare inverses. ie | 5-3] _ [1+ -ere I. °| [3 s|*%}3 2] 7 is+(18) -44i0}~ LO ! A B « Examples: a x Jo 4 beth ways Bx A > ues, both of them ove 4ho Same « Determinant of a Matrix: used to tell if a matrix has an inverse... If det(A) #0, then matrix A has an inverse. 2x2 Matrix: A= ¢ 4 det(A)= =ad-bc 3x3 Matrix: det(C)=10+0+36-0-21-16=[9 | 
