यदि `A=[(1,2,3),(-1,0,2),(1,-3,-1)],B = [(4,5,6),(-1,0,1),(2,1,2)]` तथा `C = [(-1,-2,1),(-1,2,3),(-1,-2,2)]`, सत्यापित कीजिए कि A(B + C) = AB + AC

Explanation

`B + C = [(4-1,5-2,6+1),(-1-1,0+2,1+3),(2-1,1-2,2+2)]=[(3,3,7),(-2,2,4),(1,-1,4)]`
`therefore" "A(B + C) = [(1,2,3),(-1,0,2),(1,-3,-1)][(3,3,7),(-2,2,4),(1,1,4)]`
`= [(1 xx 3 + 2(-2)+3 xx 1, 1 xx 3 + 2 xx 2 + 3(-1), 1 xx 7 + 2 xx 4 + 3 xx 4),(-1 xx 3 + 0(-2)+2 xx 1,-1 xx 3 + 0 xx 2 +2(-1),-1 xx 7 + 0 xx 4 + 2 xx 4),(1xx3+(-3)(-2)+(-1)1,1xx3-3xx2+(-1)(-1),1xx7-3 xx 4 - 1 xx 4)]`
`= [(2,4,27),(-1,-5,1),(8,-2,-9)]" "...(1)`
पुन:, `AB = [(1,2,3),(-1,0,2),(1,-3,-1)][(4,5,6),(-1,0,1),(2,1,2)]=[(8,8,14),(0,-3,-2),(5,4,1)]" "...(2)`
`AC = [(1,2,3),(-1,0,2),(1,-3,-1)][(-1,-2,1),(-1,2,3),(-1,-2,2)]=[(-6,-4,13),(-1,-2,3),(3,-6,-10)]" "...(3)`
`therefore" "AB + AC = [(8,8,14),(0,-3,-2),(5,4,1)][(-6,-4,13),(-1,-2,3),(3,-6,10)]`
`= [(8-6,8-4,14+13),(0-1,-3-2,-2+3),(5+3,4-6,1-10)]=[(2,4,27),(-1,-5,1),(8,-2,-9)]" "...(4)`
(1) तथा (4) से हमे मिलता है, A(B + C) = AB + AC