第十四讲 线性空间的同构 商空间 总结(13)

高等代数学

即有 l1α 1 + l 2α 2 + + l mα m k m +1 β m +1 k m + 2 β m + 2 k n β n = 0,∴ k m +1 = k m + 2 = = k n = 0. ∴ β m +1 + W , β m + 2 + W , , β n + W 线性无关。又设 γ + W ∈ V / W , 由于 γ ∈ V , ∴ γ = x1α 1 + + x mα m + y m +1 β m +1 + + y n β n∴ γ ∈ ( y m +1 β m +1 + + y n β n ) + W . 故 γ + W = ( y m +1 β m +1 + + y n β n ) + W .13