7.给出平面上3条直线 a1x+61y+c=0 ant+624+C2=0, a3x+b3u+C3=0 共点的充分必要条件 解：此3条直线共点的充分必要条件是相应的齐次线性方程组 41x+b1y+G12=0, a2x+b2y+e22=0, a3r+b的g+C32=0 有非零解，当且仅当系数矩阵等于0，即 a1 b C a2b2c2=0. az ba cl 8.写出通过三点(1,2)，(1，-2)，(0，-1)的圆方程 解(-22+2=5. 9.求习题3-4.3中所定义的线性子空间的维数 解设 A=(a1,a2,…,ar (1,…,c-)∈W台ca=0 9 ÷A =0÷W为AX=0的解空间 c 所以 dim W =r-rank A=r-rank(o,...,o} 习题3-7 1.求下列线性方程组的全部解 2x1-T2+5x3+7x4=0 4x1-2x2+7x4+54=0 21-I2+Ig- 54=0 2x1-x2+6x3+10z4=0 2x1+2-x3+x4=1 (2) x1+2x2+x3-x4=2 1+2+23+x4=3 107. %y 3 1.t a1x + b1y + c1 = 0, a2x + b2y + c2 = 0, a3x + b3y + c3 = 0 (0@&12. : O 3 1.t(0@&12e,Ht&@AB a1x + b1y + c1z = 0, a2x + b2y + c2z = 0, a3x + b3y + c3z = 0 Gno-, b?cbj]^V< 0,  ¯ ¯ ¯ ¯ ¯ ¯ a1 b1 c1 a2 b2 c2 a3 b3 c3 ¯ ¯ ¯ ¯ ¯ ¯ = 0. 8. ~%rN4 (1, 2), (1, −2), (0, −1) @A. : (x − 2)2 + y 2 = 5. 9. s`a 3–4.3 #Mt&￾pqF. :  αi =   a1i a2i . . . ani   , A = (α1, α2, · · · , αr). J (c1, · · · , cr) ∈ W ⇔ Xciαi = 0 ⇔ A   c1 . . . cr   = 0 ⇔ W " AX = 0 -pq #$ dim W = r − rank A = r − rank{α1, · · · , αr}.
3–7 1. st&@AB3|-: (1)    2x1 − x2 + 5x3 + 7x4 = 0 4x1 − 2x2 + 7x3 + 5x4 = 0 2x1 − x2 + x3 − 5x4 = 0 2x1 − x2 + 6x3 + 10x4 = 0 (2)    2x1 + x2 − x3 + x4 = 1 x1 + 2x2 + x3 − x4 = 2 x1 + x2 + 2x3 + x4 = 3 · 10 ·