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The rank of the following matrix $A$ is
$$
A=\left[\begin{array}{cccc}
1 & -2 & 3 & -4 \\
2 & 9 & 4 & 5 \\
4 & 5 & 10 & -3 \\
1 & 11 & -1 & 9
\end{array}\right\rfloor
$$
Options:
$$
A=\left[\begin{array}{cccc}
1 & -2 & 3 & -4 \\
2 & 9 & 4 & 5 \\
4 & 5 & 10 & -3 \\
1 & 11 & -1 & 9
\end{array}\right\rfloor
$$
Solution:
2268 Upvotes
Verified Answer
The correct answer is:
3
Given matrix $A=\left[\begin{array}{cccc}1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 4 & 5 & 10 & -3 \\ 1 & 11 & -1 & 9\end{array}\right]$
$R_3 \rightarrow R_3-\left(R_2+2 R_1\right)$ and $R_4 \rightarrow R_4-\left(R_2-R_1\right)$
or $A=\left[\begin{array}{cccc}1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & -2 & 0\end{array}\right]$
So rank
$(A)=3$.
$R_3 \rightarrow R_3-\left(R_2+2 R_1\right)$ and $R_4 \rightarrow R_4-\left(R_2-R_1\right)$
or $A=\left[\begin{array}{cccc}1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & -2 & 0\end{array}\right]$
So rank
$(A)=3$.
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