jee-main 2012 Q85

jee-main · India · offline Matrices Linear System and Inverse Existence

Let $A = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{pmatrix}$. If $u_{1}$ and $u_{2}$ are column matrices such that $Au_{1} = \begin{pmatrix}1\\0\\0\end{pmatrix}$ and $Au_{2} = \begin{pmatrix}0\\1\\0\end{pmatrix}$, then $u_{1}+u_{2}$ is equal to
(1) $\begin{pmatrix}-1\\1\\0\end{pmatrix}$
(2) $\begin{pmatrix}-1\\1\\-1\end{pmatrix}$
(3) $\begin{pmatrix}-1\\-1\\0\end{pmatrix}$
(4) $\begin{pmatrix}1\\-1\\-1\end{pmatrix}$

Let $A = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{pmatrix}$. If $u_{1}$ and $u_{2}$ are column matrices such that $Au_{1} = \begin{pmatrix}1\\0\\0\end{pmatrix}$ and $Au_{2} = \begin{pmatrix}0\\1\\0\end{pmatrix}$, then $u_{1}+u_{2}$ is equal to\\
(1) $\begin{pmatrix}-1\\1\\0\end{pmatrix}$\\
(2) $\begin{pmatrix}-1\\1\\-1\end{pmatrix}$\\
(3) $\begin{pmatrix}-1\\-1\\0\end{pmatrix}$\\
(4) $\begin{pmatrix}1\\-1\\-1\end{pmatrix}$

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