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Question

Find the Minors and Cofactors of the elements of the following determinants:
(i)∣ ∣100010001∣ ∣
(ii)∣ ∣104352012∣ ∣

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Solution


(i) A=100010001
The elements of the minor of the matrix A will be given by
M1,1=1001=1j
M1,2=0001=0
M1,3=0100=0
M2,1=0001=0
M2,2=1001=1
M2,3=1000=0
M3,1=0010=0
M3,2=1000=0
M3,3=1001=1
Hence, M=100010001
The cofactor matrix will be given by Ci,j=(1)i+jMi,j
C=100010001

(ii) B=104352012
M1,1=5212=12
M1,2=3202=6
M1,3=3501=3
M2,1=0412=4
M2,2=1402=2
M2,3=1001=1
M3,1=0452=20
M3,2=1432=14
M3,3=1035=5
Hence, M=126342120145
The cofactor matrix will be given by Ci,j=(1)i+jMi,j
C=126342120145

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