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1、JINSW立信会计学院立信会计学院数统系数统系11JINSW线性代数线性代数习题解答Jinsw22JINSW＊Ｐ１０习题１－１．３以千元为单位⎧x+x+x=10123⎪⎨x2=2x1⎪12%x+15%x+22%x=2⎩123⎧x+x+x=10123⎪⎛5515⎞⇒⎨2x1−x2=0⎜,,⎟⎝632⎠⎪12x+15x+22x=200⎩12333JINSW＊Ｐ１０习题１－１．４（２－１）⎧x=45−c−c112⎧x+x=4014⎪⎪⎪x2=c1x+x=20⎪23⎪⎪⎪x3=c2⎨x3+x6=10⇒⎨x=−5+c+c⎪x+x+x=45⎪412⎪123⎪x=20−c51⎪⎩x4+
2、x5+x6=25⎪⎪x=10−c⎩62S=45x+58x+92x+58x+72x+36x123456=3535−c+69c1244JINSW＊Ｐ１０习题１－１．４（２－２）S=45x+58x+92x+58x+72x+36x123456=3535−c+69c12x2=c1,x3=c2⇒0≤c1≤20,0≤c2≤10当c=20,c=0时，Ｓ取得最小值12S=3515min(x,x,x,x,x,x)=(25,20,0,15,0,10)12345655JINSW＊Ｐ１８习题２－１．３（３－１）0L0λ1n(n−1)0Lλ022=(−1)λλLλ12nLLLLλL00n1×(1−1
3、)(1)2n=1λ=−λ=λ1110L0λ1k(k−1)0Lλ022假定ｎ＝ｋ时，有=(−1)λ1λ2LλkLLLLλL00k66JINSW＊Ｐ１８习题２－１．３（３－２）0L0λ1k(k−1)0Lλ022=(−1)λλLλ12kLLLLλL00kn=k+10L0λ0L0λ110Lλ00Lλ02(k+1)+12=λ(−1)⋅k+1LLLLLLLLλL00λL00k+1k77JINSW＊Ｐ１８习题２－１．３（３－３）0L0λ10Lλ0(k+1)+12=λ(−1)⋅k+1LLLLλL00kk(k−1)(k+1)+12=λ(−1)⋅(−1)λλLλk+112k(k+1)k=(−
4、1)2λλLλ12k+188JINSW＊Ｐ２８习题２－２．２（１）（２－１）a+bb+cc+a111111a+bb+cc+a222222c×(−1)+ca+bb+cc+a21333333a−cb+cc+a111111a−cb+cc+a222222c+ca−cb+cc+a313333332a1b1+c1c1+a1a1b1+c1c1+a12a2b2+c2c2+a2=2a2b2+c2c2+a22a3b3+c3c3+a3a3b3+c3c3+a399JINSW＊Ｐ２８习题２－２．２（１）（２－２）ab+cc+a11111=2ab+cc+a22222c×(−1)+cab+cc+a13
5、33333ab+cc1111=2ab+cc2222c×(−1)+cab+cc323333a1b1c1a1+b1b1+c1c1+a1=2abc=a+bb+cc+a222222222a3b3c3a3+b3b3+c3c3+a31010JINSW＊Ｐ２８习题２－２．２（２）（２－１）2222a(a+1)(a+2)(a+3)2222b(b+1)(b+2)(b+3)2222c1×(−1)+cjc(c+1)(c+2)(c+3)2222(j=2,3,4)d(d+1)(d+2)(d+3)2a2a+14a+46a+92b2b+14b+46b+92c2×(−1)+cjc2c+14c+46c+9
6、2(j=3,4)d2d+14d+46d+91111JINSW＊Ｐ２８习题２－２．２（２）（２－２）2a2a+14a+46a+92b2b+14b+46b+9c22c+14c+46c+9c2×(−2)+c3d22d+14d+46d+9c×(−3)+c242a2a+1262b2b+126=02c2c+1262d2d+1261212JINSW＊Ｐ２８习题２－２．２（３）（４－１）x−10L000x−1L00LLLLLL0L0x−10000Lx−1aaaLax+ann−1n−221nn−1=x+ax+L+ax+a1n−1nn+1n−1x=0左=(−1)⋅a⋅(−1)=a=右nn13
7、13JINSW＊Ｐ２８习题２－２．２（３）（４－２）x−10L0000x−1L00xLLLLLLL0L0x−100000Lx−10aaaLax+aa+a⋅x−1nn−1n−221n−1nx≠0左−1c×(x)+c121414JINSW＊Ｐ２８习题２－２．２（３）（４－３）xx000L00L00000x0xL0−1L000LLLLLLLLLLLL00L0LL00x−10000000Lx0Lx0−1aaaan−12n−1naa＊a＊+L＊ax+a+L+aL+x+a+nnn−1n−212n−21n−1xxxxL−1c×(x)+cn−
