Question

Let $A=\left[\begin{matrix}1& 1& 1\\ 2& 2& 3\\ x& y& 2\end{matrix}\right]$ and let $V=\{(x,y,z)\in R^{3}:\det(A)=0\}$. Then the dimension of V equals}

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

A single linear constraint in $\mathbb{R}^n$ always defines a subspace of dimension $n-1$.

Answer 1

The Correct Option is C