[All Steps] Consider the homogeneous system of 2 equation in 4 unknowns with coefficient matrix
Question: Consider the homogeneous system of 2 equation in 4 unknowns with coefficient matrix
\[A=\left[\begin{array}{llll} 1 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \end{array}\right]\]- Determine a basis for the null space \(U\) of \(A\).
- Use the Gram-Schmidt process to determine a orthonormal basis of U (Show your work!)
- Show that the vector \(w=\left[\begin{array}{c}3 \\ -1 \\ 2 \\ -2\end{array}\right]\) is in U and write it as a linear combination of the orthonormal basis found above.
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