Find Ab Calculator

Find Ab Calculator

Find Ab Calculator


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Matrix subtraction is performed in much the same way as matrix addition, described above, with the exception that the values are subtracted rather than added. If necessary, refer to the information and examples above for a description of notation used in the example below. Like matrix addition, the matrices being subtracted must be the same size. If the matrices are the same size, then matrix subtraction is performed by subtracting the elements in the corresponding rows and columns:

If the matrices are the correct sizes, and can be multiplied, matrices are multiplied by performing what is known as the dot product. The dot product involves multiplying the corresponding elements in the row of the first matrix, by that of the columns of the second matrix, and summing up the result, resulting in a single value. The dot product can only be performed on sequences of equal lengths. This is why the number of columns in the first matrix must match the number of rows of the second. (Source: www.calculator.net)


The determinant of a 4 × 4 matrix and higher can be computed in much the same way as that of a 3 × 3, using the Laplace formula or the Leibniz formula. As with the example above with 3 × 3 matrices, you may notice a pattern that essentially allows you to "reduce" the given matrix into a scalar multiplied by the determinant of a matrix of reduced dimensions, i.e. a 4 × 4 being reduced to a series of scalars multiplied by 3 × 3 matrices, where each subsequent pair of scalar × reduced matrix has alternating positive and negative signs (i.e. they are added or subtracted).

We continue the process as we would a 3 × 3 matrix (shown above), until we have reduced the 4 × 4 matrix to a scalar multiplied by a 2 × 2 matrix, which we can calculate the determinant of using Leibniz's formula. As can be seen, this gets tedious very quickly, but it is a method that can be used for n × n matrices once you have an understanding of the pattern. There are other ways to compute the determinant of a matrix that can be more efficient, but require an understanding of other mathematical concepts and notations. (Source: www.calculator.net)



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