Math 3a: extra midterm review questions: a 3 3 system of linear equations represents three planes in three dimensions. The are eight general arrangements of these three planes: one resulting in a unique solution, four resulting in no solutions, and three with in nite solutions. For example, the three planes could be distinct and parallel, arranged like three sheets of paper: there is no point common to all three planes and so the system has no solutions. What are the other seven arrangements of the three planes, and draw a sketch of each: let a, b be n n matrices. If not, what should the right hand side be: consider the following system of equations x1 2x2 + x3 2x4 = 4, Find the inverse of a by using the method of row operations applied to the augmented matrix (a|i). Where a, b, c, d, e are constant scalars. By using row operations, or otherwise, nd the inverse of a.
