Coefficient determinant is zero. Reducing: R2−R1 and R3−R1 give (0,1,3,α−1) and (0,3,9,α2−1).
R3−3R2: (0,0,0,α2−3α+2).
For consistency: α2−3α+2=0, so α=1 or α=2.
The set of all values of α for which the system of linear equations
x+y+z=1
x+2y+4z=α
x+4y+10z=α2
is consistent, is
Held on 6 Aug 2022 · Verified 13 Jul 2026.
{1,2}
{−1,2}
{−1,−2}
{1,−2}
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