let K be Field; for M being Matrix of 3,K ex a, b, c, d, e, f, g, h, i being Element of K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
let M be Matrix of 3,K; ex a, b, c, d, e, f, g, h, i being Element of K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
reconsider a = M * (1,1), b = M * (1,2), c = M * (1,3), d = M * (2,1), e = M * (2,2), f = M * (2,3), g = M * (3,1), h = M * (3,2), i = M * (3,3) as Element of K ;
take
a
; ex b, c, d, e, f, g, h, i being Element of K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
take
b
; ex c, d, e, f, g, h, i being Element of K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
take
c
; ex d, e, f, g, h, i being Element of K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
take
d
; ex e, f, g, h, i being Element of K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
take
e
; ex f, g, h, i being Element of K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
take
f
; ex g, h, i being Element of K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
take
g
; ex h, i being Element of K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
take
h
; ex i being Element of K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
take
i
; M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
thus
M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*>
by MATRIXR2:37; verum