Question

Let $a=\begin{bmatrix} \frac{1}{\sqrt3} \\\ \frac{-1}{\sqrt2} \\\ \frac{1}{\sqrt6} \\\ 0\end{bmatrix}$. Consider the following two statements.
P : The matrix I4 - aaT is invertible.
Q: The matrix I4 - 2aaT is invertible.
Then, which one of the following holds ?

• A. P is false but Q is true
• B. P is true but Q is false
• C. Both P and Q are true
• D. Both P and Q are false

Answer 1

Answer: (A)

P is false but Q is true

Answer 2

The correct option is (A) : P is false but Q is true.