A real quadratic form Q=X(raise to power T)CX and its symmetric matrix C=[Cij]are said to be positive definite ifQ>0 for all(X1......Xn)=!(0......0).a necessary and sufficient condition for positive definiteness is that all the determinants C1=C11, C2=C11 C12 ;
C21 C22
C11 C12 C13
C3=C21 C22 C23 ......Cn=detC
C31 C23 C33

all positive.show that the form 4X1.X1-8X1.X2+5X2.X2 positive definite,whereas [X1 X2] 3 4 [X1]
6 2 [X2]

is not positive definite.