Question

20 1. This question deals with the following linear system of equations- 11 + 3.02 + x3 = 0 -4.x1 - 9:22 +2:03 = 0 (a) Write this system as a matrix equation Az = 7, and find the augmented matrix associated with this system. (b) Find the reduced row echelon form of the augmented matrix using elementary row operations. (c) Find the solution set for this linear system.

Answer 1

1A) linear Syltem of equations 1x + 3x2 + 1x₂ = 0 -40,- 9x2 + 2x3 = 0 (a):) Matrix equation až=8:- Combine the coefficients of x, xa, da of two equations 1 - 3 -4 -9 2 O Let A= 1 3 X= 1-4 .-9 2 23 and 3 = O So, the matrix equation is form of AR = in the x U 3 1-4 -9 2 A 2

ii) Augmented matrix A2 = 0 2=A18 3 - x= JIO 2 -4 -9 A & The augmented matrix is 3 O O -4 -9 (6) Reduced row echelon form by row operations :- The augmented matrix is elementary 3 -4 2 -9 0 R, - ist. row, R₂ and row Perforining elementary row Operations

i) R₂ = 42, + R₂ 2 -:: :) R, = R-R2 0 -5 - 1: 3 6 R₂ = Rp -5 16 is reduced row This matrix echolon form, (e) solution Set for the linear syltem write the reduced row echolon into equations x, tox25x3= 0 - form x = 5x3 ox, & IT + 2x3 = 0 - 2 - R2 = -223

1, 2, 3) = (513, -223" z = X₃ (free variable) By eq 1 x = 5x3 By eg 2 X = -2X 3 3 Answert solution set ge; 11 ng X2 50₂ 1-2x3 X2 where kj is free variable. And it has infinitely many solutions
1a) answer is in the first and second pages

1b) answer is in the 3 rd page

1c) answer is in 4 th page

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