Let \(A=\left(\begin{array}{rrr} 1 & 2 & 0 \\ 0 & 0 & -2 \\ 0 & 0 & 1 \end{array}\right)\) and define for x, y, z ∈ ℝ Q(x, y, z) = \(\left(\begin{array}{lll} x & y & z \end{array}\right) A\left(\begin{array}{l} x \\ y \\ z \end{array}\right) \text {. }\)
Which of the following statements are true?
1
The matrix of second order partial derivatives of the quadratic form Q is 2A.
2
The rank of the quadratic form Q is 2
3
The signature of the quadratic form Q is (+ + 0)
4
The quadratic form Q takes the value 0 for some non-zero vector (x, y, z)
5
Question Not Attempted