2.a,b取何值时,方程组 ar1+x2+x3=4 +bx2+x3=3 有解?在有解的情况下,求出一般解 解:(a)当a≠1且b≠0时,方程组有唯一解 2ab-4b+1 (b)当b=0时,或当a=1,b≠号时,原方程组无解 ()当a=1,b=时,一般解为n1=2-3,n=2,3是自由未知量 3.求下列齐次线性方程组的基础解系: 1+4r2+3x3+3x4+x5=0 3x1+2x2-5x3+4x4=0 +3x3-3x4=0 3x1+5x2-13x3+11x4=0 x1+x2+x3+x4+x5=0 2x1+2x2+x3+x4-2x5=0 +x4=0 x1-4x2+3x3-2x4=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) (4)(0,1,2,1) 4.证明:如果齐次线性方程组 a21x1+a222+…+a2nxn=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ak的代数余子式Ak≠0,那么 (Ak1,Ak2,…,Akn)是此齐次线性方程组的一个基础解系2. 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 ·