Invers Matriks 3 3

Invers Matriks 3 3. MethodTipsWarningsCheck the determinant of the matrix You need to calculate the determinant of the matrix as an initial step If the determinant is 0 then your work is finished because the matrix has no inverse The determinant of matrix M can be represented symbolically as det(M)[1] X Research source For a 3×3 matrix find the determinant by first To review finding the determinant of a matrix see Find Transpose the original matrix Transposing means reflecting the matrix about the main diagonal or equivalently swapping the (ij)th element and the (ji)th When you transpose the terms of the matrix you should see that the main diagonal (from upper left to lower right) is unchanged[2] X Research source Another way to think of transposing is that you rewrite the first row as the first Find the determinant of each of the 2×2 minor matrices Every item of the newly transposed 3×3 matrix is associated with a corresponding 2×2 “minor” matrix To find the right minor matrix for each term first highlight the row and column of the term you begin with This should include five terms of the matrix The remaining four terms make up the minor matrix[3] X Research source In the Create the matrix of cofactors Place the results of the previous step into a new matrix of cofactors by aligning each minor matrix determinant with the corresponding position in the original matrix Thus the determinant that you calculated from item (11) of the original matrix goes in position (11) You must then reverse the sign of alternating terms of this new matrix following the Divide each term of the adjugate matrix by the determinant Recall the determinant of M that you calculated in the first step (to check that the inverse was possible) You now divide every term of the matrix by that value Place the result of each calculation into the spot of the original term The result is the inverse of the original matrix[5] X Research source For the sample matrix shown You can follow these steps to find the inverse of a matrix that contains not only numbers but also variables unknowns or even algebraic expressions Thanks! Helpful 2 Not Helpful 0Check that your result is accurate whichever method you choose by multiplying M by M1 You should be able to verify that M*M1 = M1*M = I I is the identity matrix consisting of 1s along the main diagonal and 0s elsewhere If not you made an error somewhere Thanks! Helpful 2 Not Helpful 1Write down all your steps as it is extremely difficult to find the inverse of a 3×3 matrix in your head Thanks! Helpful 1 Not Helpful 0Computer programs exist that work out the inverses of matrices for you[19] X Research source up to and including the size of 30×30 matrices Thanks! Helpful 1 Not Helpful 0 Not all 3×3 matrices have inverses If the determinant of the matrix is equal to 0 then it does not have an inverse (Notice that in the formula we divide by det(M) Division by zero is not defined) Thanks! Helpful 1 Not Helpful 0 84% (46)Views 38M.

Find the Inverse of a 3 by 3 Matrix Online The inverse of a 3 by 3 matrix is a bit complicated task but can be estimated by following the steps given below.

3×3 Matrix Inverse Calculator Matrix Calculator

About the 3 x 3 matrix inverse calculator The inverse of a matrix can only be found in the case if the matrix is a square matrix and the determinant of that matrix is a nonzero number After that you have to go through numerous lengthy steps which are more time consuming in order to find the inverse of a matrix.

Inverse of 3 by 3 Matrix – Solved Examples

First find the determinant of 3 × 3 matrices and then find its minor cofactors and adjoint and insert the results in the Inverse Matrix formula given below \(A^{1}=\frac{1}{|A|}Adj(A)\) Where |A| ≠ 0 Learn how to find the inverse of 2 x 2 matrix here Inverse of a 3 x 3 Matrix Examples Example 1Let’s see how 3 x 3 matrix looks .