Question

(1 point) Given that the matrix [ 3 - 94 01 4 0 -6 1 1-3 -6 -36] is the augmented matrix for a linear system, use technology to perform the row operations needed to transform the matrix to reduced echelon form. Then determine if the system is consistent and if it is, find all solutions to the system. Reduced echelon form: Is the system consistent? select Solution: (21, 22, 23)=( Help: To enter a matrix use [[ ],[1] . For example, to enter the 2 x 3 matrix [1 6 2 5 3] 4 you would type [[1,2,3), (6,5,4]], so each inside set of [] represents a row. If there is no free variable in the solution, then type 0 in each of the answer blanks directly before each s. For example, if the answer is 21, 22, 23) = (5,-2,1), then you would enter (5 + 081, -2+081,1+ Osı). If the system is inconsistent, you do not have to type anything in the "Solution" answer blanks.

Answer 1

The augmented matrin of the system is 1-3 as - 3 6 Let us apply elementary row operations on Augmented matrix to reduced it to a row reduced, echelon form 13 -9 M ol Roth 3R2+4R3 1-3 -6 -3 6 13 9 4 ou 4R-3R2 -24 -30 27 + R2 13 -9 4 01 1 - 36 34 -3 - 24-30 27/ 3 -9 M ol R2-R3 o – 6 – 30 27 13 0 o -9 4 o - 6 34 - o 158 - 31/

. Reduced echelon form is. 13 -9 40 from Reduced echelon form matrin! we see that Rank op e efficient matrin (A) is eanal to the rank of Augmented matria (A) lie RCA) = R(A) Hence the system is consistent The equivalent system is a 341 - 9x2 + 4x3 = 0 - - 682 + 34 x = -1/2 158 33 = -52 - - solving the above system by Back substitution from 12 - 87 158 - for substituting xz in ③ we get ~ 6X2 + 34 x ( - 8 1/2) = -1/2

62 - - । - 34x8+ ___6x158 - - + x 87 3-058 - - - 479 पन =) 120+ 419 - ५२५ Substituting the values of X2,24 in 34 - ११ - ५४ → 34 = १( 43 । ५.१ ५५ 87 47948 2X158158 ASO+ 348 146 = 4 = - 2x 158 t 56 - + 232 - ५१3 192x158 26L 2158

79-261 x = 2x158 182 = - 9! 2x158 158 x2 = 1479 /2 - 6x474 = I2 493 - 72 - 6x 158 rov 79 - 493 6 x 158 - 414 6x158 -69 158 This the reanired solution is 781, X,Xs) = 4,594, TS153) - 8 ( tosi se to mog, 753405 FC 158 158 IS