I would appreciate having a solution written with nice handwriting and detail explanations. For example what is the definition of vector space for a matrix?

Thank you

1. For a vector subspace V of R", the orthogonal complement of V is {we R" : w . v = 0 for every v E V). Specifically, consider the orthogonal complement W of the column space of the matrix 5 2 0 4 -1 2 0 -2 -6 Show that W is a vector space and find a basis of W