1 -1 3 0-2 1 -2 1-1 -1 5 2r2+2r1,r3+r11 -1 3 00 -1 4 10 -2 8 2r3-2r21 -1 3 00 -1 4 10 0 0 0 這是梯矩陣, r(A)=2.r2*(-1), r1+r21 0 -1 -10 1 -4 -10 0 0 0 這是行簡化梯矩陣第二題 用初等行變換求逆矩陣1 0 0 0 1 0 0 01 2 0 0 0 1 0 02 1 3 0 0 0 1 03 2 1 4 0 0 0 1r2-r1,r3-2r1,r4-3r11 0 0 0 1 0 0 00 2 0 0 -1 1 0 00 1 3 0 -2 0 1 00 2 1 4 -3 0 0 1r4-r2,r2*(1/2),r3-r21 0 0 0 1 0 0 00 1 0 0 -1/2 1/2 0 00 0 3 0 -3/2 -1/2 1 00 0 1 4 -2 -1 0 1r3*(1/3),r4-r31 0 0 0 1 0 0 00 1 0 0 -1/2 1/2 0 00 0 1 0 -1/2 -1/6 1/3 00 0 0 4 -3/2 -5/6 -1/3 1r4*(1/4)1 0 0 0 1 0 0 00 1 0 0 -1/2 1/2 0 00 0 1 0 -1/2 -1/6 1/3 00 0 0 1 -3/8 -5/24 -1/12 1/4A^-1 = 1 0 0 0 -1/2 1/2 0 0 -1/2 -1/6 1/3 0 -3/8 -5/24 -1/12 1/4