Linear Algebra: Matrix and determinant

Question

For 1(a), is $p =12$ and $q = 6$?

For b(i), is the answer $a=b$ where $a$ and $b$ do not equal to 0?

for b(ii), is the answer $a\ne b$?

for b(iii), is the answer $a=b=0$ and the solution is $x=-1+t$, $y=1-t$ and $z=t$ (Let $z=t$)?

For 1(c), is $c_0=1$, $c_1=-2$ and $c_2=3$ and also the point $(-1,5)$ does not fall on the curve?

Lastly, for 1(d), is the determinant $24abcd$?

Answer 1

For b (i), you should add that $a,b$, which are equal to each other, cannot be equal to zero. For c, you seem to have the wrong coefficients (plug in $x=1$, notice something's wrong). Besides that, your answers look right to me!