3x3 Matrix Division Calculator

Matrix division is not something we encounter in our day to day lives unless you manually map arrays whilst programming for work in a field which requires complex math calculations. Moreover, this type of division is much more difficult than it seems. It would be exhausting to perform such calculations using your pen and paper. This is why iCalculator created this great online calculator to help you divide two matrices of order 3 x 3.

3x3 Matrix Division Calculator
Matrix A
Matrix B
3x3 Matrix Division Calculator Results
Matrix Division Results (A/B)

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3x3 Matrix Division Calculator. This image shows the properties and Matrix formula for the 3x3 Matrix Division Calculator

About the 3 x 3 matrix division calculator

The major condition while performing the division of two matrices is that both the matrices must have equal orders. If one matrix is of order 3 x 3, the other one should also have the same order.

To perform the division of two matrices, the first step would be to find the inverse of the matrix, which is more difficult. Who would want to put their brain into such rigorous calculations by choice when their an an online calculator to do it for you? It is better to avoid manual math calculations and save time for other commitments. If you have been looking for a good calculator for 3x3 matrix division, the good news is your search ends today as you have found an excellent calculator that outputs the calculation in seconds.

Matrices are an essential tool in mathematics and are used in various applications, from solving linear equations to machine learning. A matrix is a rectangular array of numbers, and matrix division is a fundamental operation in linear algebra. In this article, we will discuss how to divide 3x3 matrices.

Dividing 3x3 matrices can be a complex process, but by following a few simple steps, we can simplify the process. To divide two 3x3 matrices, we need to use the following formula:

A/B = A x B-1

Where A and B are the two matrices we want to divide, and B-1 is the inverse of matrix B.

To calculate the inverse of a 3x3 matrix, we need to follow these steps:

Step 1: Calculate the determinant of matrix B

The determinant of a 3x3 matrix is a scalar value that can be calculated using the following formula:

det(B) = b11(b22b33 - b32b23) - b21(b12b33 - b32b13) + b31(b12b23 - b22b13)

Where b11, b12, b13, b21, b22, b23, b31, b32, and b33 are the elements of matrix B.

Step 2: Calculate the matrix of minors

The matrix of minors is a matrix that has the same dimensions as the original matrix, and each element is the determinant of a 2x2 matrix formed by excluding the row and column of that element.

Step 3: Calculate the matrix of cofactors

The matrix of cofactors is a matrix that has the same dimensions as the original matrix, and each element is multiplied by a factor of +1 or -1 depending on its position in the matrix.

Step 4: Calculate the adjugate matrix

The adjugate matrix is the transpose of the matrix of cofactors.

Step 5: Calculate the inverse of matrix B

The inverse of matrix B can be calculated using the following formula:

B-1 = (1/det(B)) x adj(B)

Where det(B) is the determinant of matrix B, and adj(B) is the adjugate matrix of B.

Now that we know how to calculate the inverse of a 3x3 matrix, let's take an example to understand how to divide two 3x3 matrices. Suppose we have two matrices A and B, where A = [[3, 4, 5], [2, 6, 8], [1, 9, 7]] and B = [[1, 0, 2], [0, 1, 0], [1, 2, 1]]. We want to divide A by B.

Step 1: Calculate the inverse of matrix B

Using the formula we just learned, we can calculate the inverse of matrix B:

det(B) = 1(1x1 - 0x2) - 0(0x1 - 2x1) + 2(0x1 - 1x0) = -1

matrix of minors:

[[1, 0, -1], [2, 1, -2], [0, -2, 1]]

matrix of cofactors:

[[1, 0, -1], [-2, 1, 2], [0, 2, 1]]

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