determinant calculator 4x4
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Answers:I hate to tell you this but your 3X3 has a different determinant than your 4X4. It takes about 5 minutes to do a 4X4 determinant by hand, because it involves doing several 3X3's. I hope the site recommended above explains it because it is really hard to do typing in this box. Wow, I just looked at purplemath and have never seen their complicated way of doing a 3X3... and they don't even go into a 4X4. Good luck (or else use a TI-83 calculator!!!)
Answers:In general for a 4 4 matrix it may be possible to find the inverse, if the determinate is zero then it is not possible because the matrix is singular. In this case: det(A) = 0, so it is not possible.
Answers:There are several ways. The brute force solution is to calculate the 24 products corresponding to the 24 permutations of the numbers 1,2,3,4, adding or substracting them depending on the parity of the permutation. It is not practical. A practical way is to "develop" the determinant by its first column, i.e., to take te product of the i-th element of the first column by the 3x3 determinant of the matrix obtained by eliminating the first column and the i-th row, adding them all with alternating signs. |2 1 3 1| |1 0 1 1| |0 1 1 0| = |0 1 2 3| |0 1 1| |1 1 0| X 2 - |1 2 3| |1 3 1| |1 1 0| X 1 |1 2 3| The other two 3x3 determinants are multiplied by 0, and then I dropped them. I suppose that you can complete the calculation by yourself. The trick can be done using any column or row of the matrix, by remember the signs rule: if you use the second column, the first term is negative, and so one. Think on the matrix as filled of + and - signs, alternating in every column and row: + - + - - + - + + - + - - + - +
Answers:The determinant of the matrix you have given here is 80, not 75. First subtract row 2 from row 4 (which does not change det), getting; row 1: 3 5 0 6 row 2: 2 3 2 0 row 3: 2 4 0 7 row 4:-5 -1 0 3 Now pivot on [2,3] entry getting: -2 times det of the 3x3 matrix [3, 5, 6] [2, 4, 7] [-5, -1, 3] There are a variety of ways to proceed, but the det of the 3x3 is -40, so the det of your original matrix is (-2)(-40) = 80.