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Find an orthonormal basis of the kernel of the matrix \[A=\left[\begin{array}{llll}1 & 1 & 1 & 1 \\1 & 2 & 3 & 4\end{array}\right]\]...

Question

Find an orthonormal basis of the kernel of the matrix \[A=\left[\begin{array}{llll}1 & 1 & 1 & 1 \\1 & 2 & 3 & 4\end{array}\right]\]

Find an orthonormal basis of the kernel of the matrix \[A=\left[\begin{array}{llll}1 & 1 & 1 & 1 \\1 & 2 & 3 & 4\end{array}\right]\]



Answers

Find a row echelon form for the matrix.
$$\left[\begin{array}{rrr}{1} & {2} & {-1} \\ {2} & {1} & {4} \\ {-3} & {0} & {1}\end{array}\right]$$


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