A matrix is a rectangular array of numbers or symbols arranged in rows and columns. It is used in math to represent and solve systems of linear equations, perform operations on vectors, and transform geometric shapes.
To add or subtract matrices, the matrices must have the same dimensions (same number of rows and columns). Simply add or subtract the corresponding elements in each matrix to get the resulting matrix.
Matrix multiplication is a way to combine two matrices to get a new matrix. It is performed by multiplying the rows of the first matrix by the columns of the second matrix and adding the products. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
The inverse of a matrix is a matrix that when multiplied by the original matrix results in the identity matrix. To find the inverse, the original matrix must be square and have a non-zero determinant. The inverse can be found using various methods, such as Gaussian elimination or the adjugate matrix method.
Matrices have many practical applications in fields such as engineering, physics, computer graphics, and economics. They are used to solve systems of equations, calculate transformations, analyze data, and more. Some specific examples include using matrices to model traffic flow, analyze stock market trends, and design computer generated images.