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無年度 - 主題課程_行列式和線性方程式：行列式#107854
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題組內容
Let
Compute the following determinants:
(c) det
.
其他申論題
【已刪除】
#462126
【已刪除】
#462127
(a) det.
#462128
(b) det.
#462129
(d)
#462131
Let A, B, C, and D be nxn matrices with A invertible. Prove that det (det A) det() .
#462132
Given a n X n tridiagonal matrix A as below:Please find the determinant of A when n = 2020.
#462133
(a) There exist nxn real matrices A and B such that AB-BA=I, where I is then nxn identity matrix.
#462134
(b) If A and Bare nxn matrices and det(A-B)=0,then det(A)=det(B).
#462135
(c) If A is a nilpotent matrix (namely, A is an nxn matrix such that = O for some positive integer k), then det(I + A)=1 , where I is the nxn identity matrix.
#462136
Compute the following determinants: 
.
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Compute the following determinants: .