complete the linear algebra mock paper showing full solutions to each answer

complete the linear algebra mock paper showing full solutions to each answer. Every step needs to be explained to help me understand what’s being done. Also please include all formulae that will be used in each question.

This paper will include the following topics: linear equations, linear transformations, images and kernels, sub spaces and basis sets, least-squares data fitting and orthogonality, determinants, eigenvalues and eigenvectors, linear differential equations, applications of linear algebra and singular value decomposition.