Question

explanation too

Problems 7-11: The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwise state that there is no solution. State the solution in vector parametric form. In your augmented matrix, draw a vertical line that represents the equal sign, label all columns of the augmented matrix, and before each new row, write the operations that give you that new row and show the scratch work on the same page [ 1 2 -3 -6 1 7) 014 7 100 0 2] [1 2 -3 51 8) 01 4-5 10000] 110 6 31 9) 0 1 -2 -3 10000 11 4 -2 -3 11 10) 0 0 1 4 -4 (-1-4 0-5 7] [158-1 251 11) 0 0 0 -4 34 O O O 0-28)

Answer 1

LLLLL f) ri 2-3 :-67 TO) 4 7 If Azri 2-37 Augemented A =fi 2-316 101417 Ooola Lax=b is consistent iff RankAi e Rank / Augement A) 2 But This system ® is. Inconsistent because Rank A=2 and Rank AugA)=3 as 273 = - > Hence. There is no solution (8) rie-357 01 4 Loooi o Ari g -37 Pia-3157 Aug (A)=Lo1 4 151 L 0 0 0 ios consistent as Ranka= Rank Aug (11=2 System for ® is AX=6 1 0 1 I JALO0OJ

» fi 2-3 run 0 0 0 J ó ( ž J =) Htay 32=5 - Y+42 = -5 (9=-5-42 l; u=5_2y +32 n=5-86-5-42)+32 4-5-10+82732 pe=: 112-] x= 112-5 y=-42-5 - as 2 is arbitray values of we get e and y,