3 public questions tagged with this topic.
We know that solving fully: apply relevant formula, put numbers, compute. Result comes as 90°. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
In easy words, for homogeneous infinite solutions det must be zero. Det=1(-α-3)-1(α-2)+1(3+2)=-2α+4=0, so α=2. Solved completely.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
From the definition, for unique trivial solution need |A|≠0. Matrix [[2,-3],[2,α]], det=2α+6≠0, so α≠-3. Complete determinant check.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
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