This is a 3 by 3 matrix. And now let's evaluate its determinant. So what we have to remember is a checkerboard pattern when we think of 3 by 3 matrices: positive, negative, positive. So first we're going to take positive 1 times 4. So we could just write plus 4 times 4, the determinant of 4 submatrix. Instead, a better approach is to use the Gauss Elimination method to convert the original matrix into an upper triangular matrix. The determinant of a lower or an upper triangular matrix is simply the product of the diagonal elements. Here we show an example. So I'm applying the Gaussian Elimination to find the determinant for this matrix: Then, add the multiple of −3 − 3 of row 2 2 to the third row: ⎛⎝⎜1 0 0 2 1 0 0 3 −5⎞⎠⎟ ( 1 2 0 0 1 3 0 0 − 5) So the determinant I got is −5 − 5, however the answer key said it's 5 5. Some1 point out what I have done wrong? I have got a matrix with dimension 8267X4. I have to find the determinant for every 4X4 subset in the matrix to find coplanarity and i have to store the values. Kindly anyone suggest me with the solution. So another methods to find coplanarity of the points. I am looking forward for your help. Multiply this by -34 (the determinant of the 2x2) to get 1*-34 = -34. 6. Determine the sign of your answer. Next, you'll multiply your answer either by 1 or by -1 to get the cofactor of your chosen element. Which you use depends on where the element was placed in the 3x3 matrix. The inverse of a matrix A must be the unique matrix that multiplies with it to give the identity: A ⋅ A − 1 = A − 1 ⋅ A = I. Once we have calculated an inverse, we can confirm that it is WM9bL.

finding determinant of 4x4 matrix