∣λ−1λ−123λ+14λ−23λ+12λλ+33(λ−1)∣=0
R2→R2−R1
R3→R3−R1
∣λ−103−λ3λ+1λ−302λ−λ+3λ−3∣=0
C1→C1+C3
∣3λ−13−λ03λ+1λ−302λ3−λλ−3∣=0
⇒(λ−3)2[6λ]=0⇒λ=0,3
sum of values of λ=3
The sum of distinct values of λ for which the system of equations :
(λ−1)x+(3λ+1)y+2λz=0
(λ−1)x+(4λ−2)y+(λ+3)z=0
2x+(3λ+1)y+3(λ−1)z=0,
Has non-zero solutions, is ....... .
Held on 6 Sept 2020 · Verified 6 Jul 2026.
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