1.1.9 Vector Algebra

Problem: Decompose the vector \( x=(-3,5,9,3) \) into the sum of two vectors, one of which lies in the span \( \), and the other is orthogonal to this span, if \( a_{1}=(1,1,1,1), \quad a_{2}=(2,-1,1,1) \), \( a_{3}=(2,-7,-1,-1) \).