Question

Q1. (25 points) Solve the given set of linear algebraic equations X1 + 2x2 + 3x3 = 0 4x1 + 5x2 + 6x3 = 0 7x: + 8x2 + 9x3 = 0 by expressing it in the form Ax = 0 and reducing A to its row-reduced echelon form through suitable elementary row operations. Show all your work.

Answer 1

SOLUTION : x + 2x₂ + 3x3 = 0 47, + 5+2 + 6 x3 = 0 7x + 8x2 + 9 X =0 which can be written as 2 3 4 5 6 7 8 9 cohich is of the form Ax=0 where A = 2 3 4 5 6 7 8 9 Now R₂ → R2-4R, А и 12. 2 3 0-3 -6 7 8 9 R3 R3-7R, 1 2 3 0-3 -6 0-6 -12 Rzy R₂-2 R2 2 3 -3 - 6 6 O which is Row reduced echelon form

Hence complete Solution 2 3 (-3) -6 x 22 x+ 2 x2 + 3x3=0 -3X2-6x3=0 where xz is free variable assigh x₂=1 which implies > X2 = -2 and X-4 +3 = 0 = x=1 Hence T2 Rey X2 - Hence general Solution if we assiqn 23 = 23 x = x3 [1]