Question

use linear algebra methods to solve only please

2. Find the value(s) of a (if they exist) for which the system of equations has: (a) No solution. (b) One unique solution. (c) Infinitely many solutions. x + y - z = 2 x + 2y + z = 3 2x + y - 4z = a

Answer 1

solar Given system of equations x+y-Z = 2 x+2y + z = 3 20 ty-uz = a The augmented matrix is - 2 hoitoon 2 3 no 1 -4 Now, applying row R₂ R₂ - Ri operations (4) 3 2 [ALB - 2 os 2 R3 R₂ - 2 R, og ulo supinu 2 [A1B 2 a 4

R₂ R₂ of Rg 1 - 2 -> » [A1B] 2 1 0 a-3 (a) for no solution ela) + elAB) (e rank) Here, 2007 eCA) = 9 - eLAB) 3 a-3 to at3 (b) for unique solution (CA) = e(AB) 3. But here EQA) = 3 so, there no value of a such that the given system of equations has a unique solution

(c) for infinitely many solutions CLA) = P(AB) +3 Here, eCA)=2 e(AB) =2 a-3 ro sa=3 ia

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