Question

Find a basis for the vector space W spanned by the vectors

$$ \overrightarrow{v_{1}}=(1,2,3,1,2), \overrightarrow{v_{2}}=(-1,1,4,5,-3), \overrightarrow{v_{3}}=(2,4,6,2,4), \overrightarrow{v_{4}}=(0,0,0,1,2) $$

(Hint: You can regard W as a row space of an appropriate matrix.)

Using the Gram-Schmidt process find the orthonormal basis of the vector space W from the previous question

Let \(\vec{u}=(2,3,4,5,7)\). Find pro \(j_{W} \vec{u}\) where \(\mathrm{W}\) is the vector subspace form the previous two questions.