Question

If `2a x-2y+3z=0,x+a y+2z=0,a n d2+a z=0` have a nontrivial solution, find the value of `adot`

Answer 1

for nontrivial solution we must have
`|{:(2a,,-2,,3),(1,,a,,2),(2,,0,,a):}|=0`
`" or " 2a(a^(2) -0)+2(a-4)+3(0-2a)=0`
`" or " 2a^(3)+2a-8 +0 -6a=0`
`" or " 2a^(3)-4a-8=0`
` " or " a^(3)-2a -4=0`
` " or "a^(3) -2a^(2) +2a^(2)-4a+2a -4=0`
`" or "a^(2)(a-2)+2a(a-2)+2(a-2)=0`
`" or "(a-2)(a^(2)+2a+2)=0`
`" or "a=2`