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We would like to find the determinant for matrices of the following form.
00:04
For an n -by -n -n -square matrix, we consider a matrix where all the entries are one, except for those directly below the diagonal.
00:15
To be explicit, we write down here the first few examples for n being 1, 2, 3, 4, and 5.
00:22
The first two cases, n equals 1, and 2 are trivial.
00:27
The determinant are both 1.
00:29
For n equal 3 or higher, we should help to find some recursive relation relating the determinant of p n to letter p n minus 1.
00:42
If we consider the laplace expansion of the matrix down the first column, we notice that the first term would be, for instance, if we look at p5, the first turn in this, in this...