Question

Let $A=\begin{pmatrix} 1 & 1 \\\ 0 & 1 \\\ -1 & 1 \end{pmatrix}$and let AT denote the transpose of A. Let $u=\begin{pmatrix} u_1 \\\ u_2 \end{pmatrix}$ and $v=\begin{pmatrix} v_1 \\\ v_2 \\\ v_3 \end{pmatrix}$be column vectors with entries in $\R$ such that $u^2_1+u_2^2=1$ and $v_1^2+v_2^2+v^2_3=1$. Suppose
$Au=\sqrt2v$ and $A^Tv=\sqrt2u.$
Then |$𝑢1 + 2 \sqrt2 𝑣_1$| is equal to _________. (Rounded off to two decimal places)

Answer 1

The correct answer is : 3.