Let c-jk denote the cofactor of the row j, column k entry of the matrix A
belong to M(nxn)
a.
Prove that if B is the matrix obtained from A by replacing column k by e-j,
then det(B)=c-jk。
b.
Show that
c-j1
c-j2
A* .... =det(A)*e-j
....
c.
If C is the nxn matrix such that C-ji =c-ij,then AC=[det(A)]*In
d.
If det(A)!=0,then A^-1= [det(A)]^-1 *C
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