2.a,b取何值时，方程组 a1+2+xg=4 x1+b证2+x%=3 1+20z2+23=4 有解在有解的情况下，求出一般解 解(a)当a≠1且b≠0时，方程组有唯一 b-1 (=a-可 =6 =2 (b)当6=0时，或当a=1,b≠号时，原方程组无解 (C)当a=1,b=号时，一般解为：x1=2-x3,2=2,x3是自由未知量 3.求下列齐次线性方程组的基础解系 x1+工2+工3+工4+T5=0 3知1+22+x3+x4-6=0 51+42+33+34+6=0 2+2x3+2x4+4红5-0 3x1+2x2-53+4z4=0 (2){3x1-x2+3g-3z4=0 3z1+5r2-13rg+11z4=0 1+++4+=0 2x1+22+3+x4-2=0 5z1+4红2-33+4红4+5=0 x2+6-4-45=0 [x1-2x2+3z3-4z4=0 2-3+4=0 x1+3x2 -3z4=0 x1-4z2+3x3-2z4=0 解(1)(1，-2,1,0,0，(1，-2,0,1,0)(3，-4,0,0,1 (2(-1,24,9,0).(2,-21,0,9). (3)(-7,7,-1,1,0),(-25,28,-4,0,1) (4)(0,1,2,1). 4.证明：如果齐次线性方程组 a111+a122十…+a1nn=0 a211+a222+…+a2mn=0 +=0 的系数矩阵A的行列式|4=0，方程组的秩是n-1,并且矩阵A中au的代数余子式A知≠0，那么 (41,Ak2,…,A)是此齐次线性方程组的一个基础解系。 82. a, b zR, @AB    ax1 + x2 + x3 = 4 x1 + bx2 + x3 = 3 x1 + 2bx2 + x3 = 4 G-? kG-!, s%H}-. : (a) b a 6= 1 ? b 6= 0 R, @ABG,H-:    x1 = 2b − 1 b(a − 1) x2 = 1 b x3 = 2ab − 4b + 1 b(a − 1) ; (b) b b = 0 R, Db a = 1, b 6= 1 2 R, K@AB,-; (c) b a = 1, b = 1 2 R, H}-": x1 = 2 − x3, x2 = 2, x3 gNz . 3. sHt&@ABz-j: (1)    x1 + x2 + x3 + x4 + x5 = 0 3x1 + 2x2 + x3 + x4 − x5 = 0 5x1 + 4x2 + 3x3 + 3x4 + x5 = 0 x2 + 2x3 + 2x4 + 4x5 = 0 (2)    3x1 + 2x2 − 5x3 + 4x4 = 0 3x1 − x2 + 3x3 − 3x4 = 0 3x1 + 5x2 − 13x3 + 11x4 = 0 (3)    x1 + x2 + x3 + x4 + x5 = 0 2x1 + 2x2 + x3 + x4 − 2x5 = 0 5x1 + 4x2 − 3x3 + 4x4 + x5 = 0 x2 + 6x3 − x4 − 4x5 = 0 (4)    x1 − 2x2 + 3x3 − 4x4 = 0 x2 − x3 + x4 = 0 x1 + 3x2 − 3x4 = 0 x1 − 4x2 + 3x3 − 2x4 = 0 : (1) (1, −2, 1, 0, 0), (1, −2, 0, 1, 0), (3, −4, 0, 0, 1). (2) (−1, 24, 9, 0), (2, −21, 0, 9). (3) (−7, 7, −1, 1, 0), (−25, 28, −4, 0, 1). (4) (0, 1, 2, 1). 4. ST: Ht&@AB    a11x1 + a12x2 + · · · + a1nxn = 0 a21x1 + a22x2 + · · · + a2nxn = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . an1x1 + an2x2 + · · · + annxn = 0 j]^ A  ) |A| = 0, @AB  n − 1, W?]^ A  akl Q$￾) Akl 6= 0, 0 (Ak1, Ak2, · · · , Akn) OHt&@ABHfz-j. · 8 ·