Question

Need help with c). Any help would be greatly appreciated

Let A be a square matrix and b be a vector and consider the system Ax = b. Gaussian elimination changes Ax = b to Rx = C, where R is the reduced row-echelon form of A. The solutions to this system are of the form 21 ouw X=1 +11+z1 for any real numbers y and z. 1. Find Randc 2. The row operations taking A to R are the following: i. Subtract 2 times row 1 from row 3 ii. Subtract row 1 from row 4 iii. Add 5 times row 2 to row 4 Find the matrix Fsuch that R = FA. 3. Find A and b.

Answer 1

We have solved all the problems.

Criven that, Ax=b » Rx= e Reduced Row - Echelon foorm. X + 2 + z 5 firest. second special vector special vector. now-echelon form, then, 0 Since R is reduced for y=0, z=0 in a Noo for R . in a special solution provide Other two vectors i Rank of R = 4 -2 . 4 = dimension of R . 2= no. of special vectors in = 2 . echelon form, and ranck of R must be all o. and top. Since, R is in reduced row in R, the bottom two rows two rows one, [lo –4 +3 ] and [o iz us] 290 m Joring first 2nd special vector. from first. special vector drom. Second special . rector . special veeton - o: R - -4 37 -2 -5 1 0 0 0 0 0

© E E. E Full Eu Ezi det. I = To i ool Co City Lo oo where tur Tol o ol [Euz is obtained by adding "5 times of now 2 to of I" to "grow u of I". Po 5 ou E4 = Too 07 oi oo oo lo [En, in obtained by subtracting | "How I of I" from "How 4 of I" | subtract Tolool from. lo 10 E31 is obtained by 1"2 times row I of I" "row 3 of I" mes row 1 od 1 ou troching . f = Eu Eu Ezi ooo Tio 007 T oo looolxlo ioololo lool lo o lol Toolololol 05 O LooLooo computed in MATLAB 12i 0 1 5 0 1 - oin

0 R=FA A=F-R and and c=Fb. b=fte - How T o o o o o] o ol 2 o io 1 -5 0 [computed in MATLAB] • A - 0 نیا 0 0 1 o 2 1 0 0 0 0 0 1 0 0 -4 -2 0 0 0 0 - 5 Lo T 0 -od J 0 1 0 5 -4 -2 -8 6 3 -sl 6 28 [Computed in MATLAB DO Li : b = o - ON oo-O oo- – o 0 us 1 o 0 0 I LoJ Computed in MATLAB