A book I have been reading and solving problems in for the last 21 months. Linear Algebra, Schaum's Outlines, Marc Lipson, Ph. D., Seymour Lipschutz, Ph. D., 2018, McGraw-Hill Education. This (instructional) book aligns with Beginning Linear Algebra, Linear Algebra, Advanced Linear Algebra, Advanced Physics, Advanced Engineering, and Quantitative Analysis. See below for photos of step-by-step complete solution to problem number 7.75 contained within in chapter 7, "Inner Product Spaces and Orthogonality," found in this book. A photo of the problem, and a photo of the correct solution (photos of the actual book) are provided on this webpage. -Mark R. Rowe

Let U be the subspace of R^(4) spanned by, v1 = (1,1,1,1), v2 = (1,-1,2,2), v3 = (1,2,-3,-4).

I applied the Gram-Schmidt Algorithm to find an orthogonal and orthonormal basis, and computed the projection of v = (1,2,-3,4) onto U.

-Mark R. Rowe