A linear equation is an algebraic equation that involves two or more variables and can be written in the form y = mx + b, where m is the slope and b is the y-intercept. It represents a straight line on a graph.
To solve a system of linear equations, you can use the elimination, substitution, or graphing method. In the elimination method, you eliminate one variable by adding or subtracting equations. In the substitution method, you solve for one variable in terms of the other and then substitute into the other equation. In the graphing method, you plot the equations on a graph and find the point of intersection.
A matrix is a rectangular array of numbers or variables arranged in rows and columns. It is often used to represent a system of linear equations or to perform operations such as addition, subtraction, and multiplication.
To add or subtract matrices, they must have the same dimensions. You simply add or subtract the corresponding elements in each matrix to get the resulting matrix. For example, to add two matrices A and B, you add Aij to Bij to get the element in the same position in the resulting matrix.
The inverse of a matrix is a matrix that, when multiplied by the original matrix, gives the identity matrix. It is denoted by A-1 and is only defined for square matrices with non-zero determinants. The inverse of a matrix can be found using various methods such as Gauss-Jordan elimination or the adjugate matrix method.