請問ㄧ題矩陣數學題！?

Q
= (x1)² + 9(x2)² - 3(x3)² - 8x1*x2 - 2x1*x3 + 8x2*x3 - 2x1 - 6x2 + 2x3
= (x1)² + 9(x2)² - 3(x3)² + 2( - x1 - 3x2 + x3 - 4x1*x2 - x1*x3 + 4x2*x3 )
= x^T * A * x

其中
x = [ 1 x1 x2 x3 ]
x^T 表示 x 的轉置( transpose )矩陣
A =
[ 0 -1 -3 1 ]
[ -1 1 -4 -1 ]
[ -3 -4 9 4 ]
[ 1 -1 4 -3 ]

計算 A 之主子矩陣( principal submatrix ) 得 :
C1 = 0
C2 = - 1
C3 = - 42
C4 = 168
故 Q 為不定

Ans: 此式為不定, 即正負號不一定.