# MATH 125 Study Guide - Final Guide: Row Echelon Form, Invertible Matrix, Diagonal Matrix

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Notes: some steps are skipped in the solutions below (e. g. , some row reduction of matrices is omitted). In your exam, you should show all your work! Remember also that there are often a number of ways to solve a given problem; here i have generally just given one method: (9 points) compute the determinant of q, where. = 1( 20) = 20. (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (expand along 1st column) (r1 + r2) (expand along 1st column: consider the matrices. Given that b is the reduced row echelon form of a: 5 (c) the reduced row echelon form of the augmented matrix of the homogeneous system a~x = ~0 is equal to [b|~0], i. e. , Thus, there are three leading variables in this system (x2, x3 and x5), and the remaining variables (x1, x4) are free. Assigning the parametric values s and t to the free variables x1 and x4, respectively, we get that the general solution of a~x = ~0 is.