Question

Using properties of determinants, prove that

|(a,a+b,a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c)|=a³

Answer 1

[c₁ = c₂ in second det.]

Expanding along R₁ we get
= a³ .1(7 - 6) - 0 + 0
= a^{3 .}