8设A11
04401337B53411215
3213求A1B3322
输入ClearABA3044213315341215B032713133122I
versemaBMatrixForm输出为
6191625938918355169169838716
对于线性方程组AXb如果A是可逆矩阵Xb是列向量则其解向量为A1b例19解方程组xy3z6输入ClearAbA321113244b762I
verseAb输出为112求方阵的行列式
35求行列式D21110512341133
3x2yz72x4y4z2
例110
输入ClearAA3112513420111533DetA输出为40
a2
1a21b21c1
2
abcd
例111求D
b2c2d
2
d2
1a1b1c1d
1111
输入ClearAabcdAa21a2a1a1b21b2b1b1c21c2c1c1d21d2d1d1
fDetASimplify则输出
abacbcadbdcd1abcda2b2c2d2
1x12例112计算范德蒙行列式x1
3x14x1
1x22x2
3x24x2
1x32x3
3x34x3
1x42x4
3x44x4
1x52x5
3x54x5
输入ClearxVa
Tablexjkk04j15MatrixForm输出为
1x1x12x134x11x2x22x23x241x3x32x33x341x4x42x43x441x5x52x53x54
再输入Detva
则输出结果比较复杂项很多若改为输入Detva
Simplify或FactorDetva
则有输出x1x2x1x3x2x3x1x4x2x4x3x4x1x5x2x5x3x5x4x5
37例113设矩阵A1125726403求AtrAA376
942569783790
输入A37264794201156932783757906MatrixFormADetATrAMatrixPowerA3MatrixForm则输出AtrAA3分别为115923
72618481713174380131502218358228404984451122238426664777451252062944263129415161006
向量的内积
f向量内积的运算仍用“”表示也可以用命令Dot实现例114求向量u123与v110的内积输入u123v110uv输出为1或者输入Dotuv所得结果相同
实验习题
2311111设A111B124求3AB2A及AB111051
2设A01求A10一般地Akk是正r