a=2

b=9

c=7

d=5

please there was one tutor name RemaS who started the first part if you could tag him to continue the second part.

6:57 270Exam1A V Done You may talk to anyone Due by 2359 hours on 20230919 270 Exam 1A 6 (1b) "& = a'nA ouijaal (0) u.v : aulv1 - buzv2 - Cu3V3 - du4V4 (1) lull2 := u.u (2) (prp (u , V ) : (2 .0 = 0 ) My u.v = ( )ujv1 + ( )uzvz + ( )u3V3 + ( )UAV4 My Hull? = u.u = ( ) ( u,)2 + ( ) ( 22)2 + ( )(23)2 + ( )(24)2 Circle correct choices from among Y, N, Proof, and Witness and provide, showing work on the facing side, a proof or witness or both as the case may be: Define u := My u = 1 (i) 2 (ii) DE ( . ) 1 8 pre ( 1. ) Y N Pf W 3 (iii) .H EnA Y N Pf W u=0 109 You may talk to anyone Due by 2359 hours on 20230919 270 Exam 1A Q A ...6:57 I '9' @' 270Exam1A v Done 110 You may talk to anyone Due by 2359 hours on 20230919 270 Exam 1A 5 (1c) Write answers on this side and show work on pages following this one numbered 1120, 1121, etc. using as many as you need. Define: S := {(x, y) e R2 ax+by+c=0} My S := '(x,y) E [R2 ( )x+( )y+( Note that P and Q are required to be distinct points \_/ H O W 1 (i) Find P I: (Pppz) = ( , ) E 5 and prove your asertion. 1 (ii) Find Q == (111: 1h) = ( , ) E S and prove your assertion. 3 (iii) Decide if S 2 SL (P, Q) that is, if the striaght line through the points P and Q is precisely the set 5. Y N Pf W 111 You may talk to anyone Due by 2359 hours on 20230919 270 Exam 1A Q Q 69 [3' 6-57 I '9' @' 270Exam1A v Done Lu You may talk to anyone Due by 2359 hours on 20230919 270 Exam 1A 6 (2a) You will not get any points on this page unless you can do part (v) and part (vi) completely and exhibit exact calculations with all details. Fill in the blanks with real numbers to express the answers in the forms indicated. Write answers on this page and do all your work on pages following this one and numbered 1140, 1141 etc Note that: k, l, m, n,p, q,r,s E R 1(i) 11:23; 10+"? ( )+i( ) U _= a+ic = [-1 = ( ) i( ) 1 (u) u . Mid ice 8 b 'd . . 1(iii) 12:: H. = T+tS = ( )+1( ) a+Lc 1 (iv) := b'l'l'd = mein = ( )el( ) a+lC 1 (v) (p + iq) (1' + is) 1 Y N Pf W 1 (vi) (keil) (main) = 1 Y N Pf W 113 You may talk to anyone Due by 2359 hours on 20230919 270 Exam 1A Q Q 69 [3' 6-57 I '0' @' 270Exam1A v Done 114 You may talk to anyone Due by 2359 hours on 20230919 270 Exam 1A 6 (2b) Solve the following system of equations for x and y/ in RV, by row-reduction. Write your answers on this page and show your work for row-reduction on pages following this one numbered 1160, 1161 etc. Check that your solution is correct exactly as shown in the notes; otherwise, you will get 0 on this question. 4(i) ax+dy=a+d bx+ cy = b+c ()X+( )y=( )+( )=() ()x+( )y:( )+( )=() My problem: x: y: 1(ii) The solution requires parameters, and therefore represents a - flat, also called a 1 (iii) Have you checked, exactly as in the notes, that your solution is correct. Otherwise, you will not get any points on (2b). Circle an appropriate letter. 115 You may talk to anyone Due by 2359 hours on 2080919 270 Exam 1A Q Q (39 a 6:57 270Exam1A V Done Tou may tai t anyone Due by 2359 hours on 20230919 270 Exam 1A 5 (2c) Consider a subset of the plane R2, that is, SE P IR2 ) such that: P := (a, b ) and Q = (b, a) My P := ( ) and my Q = ( k + 1 # 0) SL P , Q = ( x , y ) ER2 3k , LER A (x = P1 + (91 ) k+l ( y = kp2 + 192 k+l My SH. ( ( ) . ( ) ) (k + 1 # 0) k+ l ( y = k ( ) + ( ) Decide if: Stun SL P, Q , that is the set SL P, Q is a straight line in the sense of the predicate StLn. Y N Pf W 118 You may talk to anyone Due by 2359 hours on 20230919 270 Exam 1A Q A ...6-57 I '9' E) 270Exam1A v Done 120 You may talk to anyone Due by 2359 hours on 20230919 270 Exam 1A 6 (3a) Find the Hermite form HF(A)of the matrix: A1 A2 A3 A4 A5 A6 A7 A6 A5 A4 A3 A2 A3 A4 A5 A6 A7 As = I 1 Use the row reductions on: A A1 A2 A3 A4 A5 A5 1 O 0 A7 A6 A5 A4 A3 A2 0 1 0 3 A4 A5 A6 A7 A8 0 0 1 and obtain the matrix P such that PA 2 HF (A) Start the work for raw- reduction on the facing side and check that your solution is correct exactly as shown in class by computing PA; otherwise, you will get no points on this question. HF(A) || , |l PA || , |l 121 You may talk to anyone Due by 2359 hours on 2030919 270 Exam 1A Q Q a Due by 2359 hours on 20230919 270 Exam 1A 5 (3c) Decide if: d 3 SA R2 StLn S StLn2 S Y N Pf W 126 You may talk to anyone