Oct 19, 2016 · Solving a System of Linear Equations By Using an Inverse Matrix Consider the system of linear equations \begin{align*} x_1&= 2, \\ -2x_1 + x_2 &= 3, \\ 5x_1-4x_2 +x_3 &= 2 \end{align*} (a) Find the coefficient matrix and its inverse matrix. (b) Using the inverse matrix, solve the system of linear equations. (The Ohio […] In linear algebra, matrix equations are very similar to normal algebraic equations, in that we manipulate the equation using operations to isolate our variable. However, the properties of matrices restrict a few of these operations, so we have to ensure that every operation is justified.Sparse matrix linear-equation solver, using the conjugate gradient algorithm. Note that the technique only applies to matrices that are symmetric and positive-definite. S = solve (eqn,var) solves the equation eqn for the variable var. If you do not specify var, the symvar function determines the variable to solve for. For example, solve (x + 1 == 2, x) solves the equation x + 1 = 2 for x.