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# determinant calculator 4x4

Question:Hi... I need to find the determinant of a 4 x 4 matrix. Here's where I started: -1 0 1 -4 -3 3 0 5 1 0 2 0 -2 0 6 2 Next I multiplied row 2 by 1/2, therefore changing row 2 to: -3/2 1 0 5/2 I then eliminated row 2 & column 2 to leave me with a 3 x 3 reading: -1 1 -4 1/2 2 0 -1 6 2 Now I'm stuck!! How do I multiply this out to find the determinant? I can handle a 2 x 2, but not this! Thanks!

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!!!)

Question:part of our algebra homework was to find the inverse of a matrix that looks like this... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 any help at all would be appreciated **and don't try to suggest putting it in my calculator and clicking the inverse button. i've tried it and it doesn't work

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.

Question:2 1 3 1 1 0 1 1 0 1 1 0 0 1 2 3 How do i find the determinant of such matrix? i know how it has something to do with a minors and cofactors but have no idea? please help explain this!

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: + - + - - + - + + - + - - + - +

Question:whats the easiest way to find the determinant of a 4x4 matrix? I think I'm supposed to end up removing a row and a column to get a 3x3 matrix, but I'm not sure what to select as my pivot?? here's an example: row 1: 3 5 0 6 row 2: 2 3 2 0 row 3: 2 4 0 7 row 4:-3 2 2 3 i selected the 2 in the 2nd row, 1st column, then i reduced that column which obviously changed the other #s. I then got 2 (-1)^3 multiplied by the new 3x3 matrix determinant which was -150. My answer is supposed to be 75. I know i get 75 if i devide the 2 numbers but i dont think that's how it's done. help much appreciated

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.