[線代] nonsingular

看板Math作者 (無法顯示)時間14年前 (2011/05/05 23:46), 編輯推噓2(2推 0噓 1→)
留言3則, 1人參與, 最新討論串1/1
let A be a 3*3 matrix and let x1, x2 and x3 be vector in R^3 show that if the vectors y1 = Ax1 y2 = Ax2 y3 = Ax3 are linearly independent, then the matrix A must be nonsingular and the vector x1, x2 and x3 must be linearly independent 請問這要怎麼證明呢? 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 61.228.26.160
推
05/05 23:50, , 1F
可知 k1*y1+k2*y2+k3*y3=0 => k1=k2=k3=0
05/05 23:50, 1F
→
05/05 23:51, , 2F
把上示用題目帶入 假設A is singular
05/05 23:51, 2F
推
05/05 23:53, , 3F
應該可以得到矛盾
05/05 23:53, 3F
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