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If the sequence A1, A2, A3 and A4 are proportional and A1A2 = - 323, a2a3 = - 24, then q = 0___ ．
∵ A1A2 = - 323, a2a3 = - 24, ∵ a1a2a3 = a1a3 = 1q2 = 49 ∵ q = ± 32, so the answer is: ± 32
Calculate the determinant of order n + 1, DN + 1 = [x A1 A2 A3... An; A1 x A2 A3... An; A1 A2 x A3... An;...]
a1 a2 a3 a4 ...x]
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Calculation: DN = / 1 + A1 1... 1 / / 1 1 + A2... 1 / / 1... 1 + an /, where A1A2... An is not equal to 0
1+a1 1 ...1
1 1+a2 ...1
......
1 1 ...1+an
Multiply line 1 by - 1 and add to the rest of the lines
1+a1 1 ...1
-a1 a2 ...0
......
-a1 0 ...an
The k-th column proposes AK, k = 1,2,..., n (note that AI is not equal to 0) to obtain a1a2a3... An*
1+1/a1 1/a2 ...1/an
-1 1 ...0
......
-1 0 ...1
Add columns 2 to n to column 1 to get an upper triangular determinant
Determinant = a1a2a3... An (1 + 1 / A1 + 2 / A2 +... + 1 / an)
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