In mathematics, a matrix (plural matrices) is a rectangular array[1]—of numbers, symbols, or expressions, arranged in rows and columns[2][3]—that is treated in certain prescribed ways. One such way is to state the order of the matrix. For example, the order of the matrix below is 2x3, because there are two rows and three columns. The individual items in a matrix are called its elements or entries.
Provided that they are the same size (have the same number of rows and the same number of columns), two matrices can be added or subtracted element by element. The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second
Determinants:
Let’s assume the example of matrix B:
The determinant of matrix B or |B| would be 4 x 6 – 6 x3. This would give the determinant as 6.
.The determinant is a real number, it is not a matrix.
- The determinant can be a negative number.
- It is not associated with absolute value at all
except that they both use vertical lines.
- The determinant only exists for square matrices
(2×2, 3×3, ... n×n). The determinant of a 1×1 matrix is that
single value in the determinant.
- The inverse of a matrix will exist only if the
determinant is not zero.
Applications of
matrices in business.
- Matrices are used in representing the real world data's like the traits of peoples' population, habits, etc. They are best representation methods for plotting the common survey things.
- Matrices are used in calculating the gross domestic products in economics which eventually helps in calculating the goods production efficiently.
- In robotics and automation, matrices are the base elements for the robot movements. The movements to the robots are programmed with the calculations of matrices's row and columns. The inputs for the controlling robots are given based on the calculations from matrices.
