Consider the following linear system x+2y+2z=1(1), x+ay+3z=3(2), x+11y+az=b(3)

figoveck38

figoveck38

Answered question

2022-11-18

Consider the following linear system
(1) x + 2 y + 2 z = 1
(2) x + a y + 3 z = 3
(3) x + 11 y + a z = b

Answer & Explanation

Liehm1mm

Liehm1mm

Beginner2022-11-19Added 13 answers

(1) x + 2 y + 2 z = 1
(2) x + a y + 3 z = 3
(3) x + 11 y + a z = b
Solve y , z from (1) and (2) and substitution of it into (3) leads to:
(4) ( 33 + a 2 + 6 b 2 a ( 3 + b ) ) 2 ( a 3 ) + 5 + 4 a a 2 2 ( a 3 ) = g ( a , b ) + f ( a ) x = 0
(1) If f ( a ) = g ( a , b ) = 0, then x can take any values.
(3) If g ( a , b ) = 0, f ( a ) 0, then x = 0.
(3) If g ( a , b ) 0, f ( a ) = 0, then x has no solution.
(4) If g ( a , b ) 0, f ( a ) 0, then x has one solution, x = g ( a , b ) f ( a )

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