Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Linear Algebra Bilinear Forms,Quadratic Forms
Consider the quadratic form Q(x, y, z) associated to the matrix
B = \(\left[\begin{array}{ccc} 1 & 1 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & -2 \end{array}\right]\)
Let
S = \(\left\{\left[\begin{array}{l} \rm a \\\rm b \\\rm c\end{array}\right] \in \rm ℝ^3 \mid Q(a, b, c)=0\right\}\).
Which of the following statements is FALSE?
1
The intersection of S with the xy-plane is a line.
2
The intersection of S with the xz-plane is an ellipse.
3
S is the union of two planes.
4
Q is a degenerate quadratic form.