求下列矩阵的特征值及特征向量的求法.[tex=9.357x3.643]sSXBpxJWudVpH1R35o4LnIcNXurDIqYZ4dH4l1OxViDlMo63aWtGmjOJfggNcg2JAG1+id3IY+5tegzyiTGaIx/fU35O3sDSe4zpVxssfPqSlAUc3qokxvUpT+Dk6ilJ[/tex]
求下列矩阵的特征值及特征向量的求法.[tex=9.357x3.643]sSXBpxJWudVpH1R35o4LnIcNXurDIqYZ4dH4l1OxViDlMo63aWtGmjOJfggNcg2JAG1+id3IY+5tegzyiTGaIx/fU35O3sDSe4zpVxssfPqSlAUc3qokxvUpT+Dk6ilJ[/tex]
已知 3 阶矩阵[tex=9.357x3.643]3BT1BgBZQ5uJXxD5dg+w206nRicbP0ehfsdm402BEahOSFRaJ80S6Pq7C5Cknxl9Y6aY+nTw69xHAOkPZ2f212ZZz8QHDW+Ef0YXLFQv4XccEsbPPuTi2OwLP39EbgWB[/tex],求[tex=2.214x1.214]H8C97L9EbcJl/08XS7qu+w==[/tex]
已知 3 阶矩阵[tex=9.357x3.643]3BT1BgBZQ5uJXxD5dg+w206nRicbP0ehfsdm402BEahOSFRaJ80S6Pq7C5Cknxl9Y6aY+nTw69xHAOkPZ2f212ZZz8QHDW+Ef0YXLFQv4XccEsbPPuTi2OwLP39EbgWB[/tex],求[tex=2.214x1.214]H8C97L9EbcJl/08XS7qu+w==[/tex]
解矩阵方程[tex=3.143x1.0]1fpwrNejNv38wxblrXj6lg==[/tex],其中[tex=9.357x3.643]sSXBpxJWudVpH1R35o4LnA8P+MOnELws9A5zsd8AHnhvjeMfeNWOAY0szY9VbvnVYCJUrQPgAkbR0gMd56Xz6C4Zr6hOh0QSgoozgHW6WvtqPtH9L3B/bFjcoVq0HFCG[/tex],[tex=8.5x2.786]tAg4kjefm91yBdigy4ffjF19BWEGocSZLeYfHUZWVe2RgMXMUa+vdE30x+1Mao39bbfqXzdrz64xL0lEqqGG5+Hqu14IHOSH11e02fD3N74=[/tex] .
解矩阵方程[tex=3.143x1.0]1fpwrNejNv38wxblrXj6lg==[/tex],其中[tex=9.357x3.643]sSXBpxJWudVpH1R35o4LnA8P+MOnELws9A5zsd8AHnhvjeMfeNWOAY0szY9VbvnVYCJUrQPgAkbR0gMd56Xz6C4Zr6hOh0QSgoozgHW6WvtqPtH9L3B/bFjcoVq0HFCG[/tex],[tex=8.5x2.786]tAg4kjefm91yBdigy4ffjF19BWEGocSZLeYfHUZWVe2RgMXMUa+vdE30x+1Mao39bbfqXzdrz64xL0lEqqGG5+Hqu14IHOSH11e02fD3N74=[/tex] .
用Housseholder变换作如下矩阵[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的QR分解[tex=9.357x3.643]3BT1BgBZQ5uJXxD5dg+w28DL5HPS9xGP+qGepKS5l4xbLRVF+lJWuVmDFQ5fkVpVJUXGTl/Halu2nqIC5dHUY2lywlmo+b5IUWRH9AwBzcZgWXMO+qA6AvgVxMZqt0E0[/tex].
用Housseholder变换作如下矩阵[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的QR分解[tex=9.357x3.643]3BT1BgBZQ5uJXxD5dg+w28DL5HPS9xGP+qGepKS5l4xbLRVF+lJWuVmDFQ5fkVpVJUXGTl/Halu2nqIC5dHUY2lywlmo+b5IUWRH9AwBzcZgWXMO+qA6AvgVxMZqt0E0[/tex].
解矩阵方程:设[tex=5.786x1.286]Mkuj34GAx0A1tlDpp+qnbg==[/tex], 其中[tex=9.357x3.643]r+tiAx6ClSaeP7cZbqpjmSQknJTvSyjmMn9KQrSttYf3zIfQ34uJf77prkHVmwBtUg1sQm/L+OX93K1V8lyVP6AnIkBa61KybF7Ps1O0+BW8dQxffy6Y25XUk5WfKhz3[/tex], [tex=4.786x3.5]t4TU5HQAVYrwy1dmvaCPG6gR9A0QcoABryDcNsMl4hWdCUY/tB7stPt/A+U6KTtsxs0wap+GUSbNmlzM8f2VIg==[/tex]。
解矩阵方程:设[tex=5.786x1.286]Mkuj34GAx0A1tlDpp+qnbg==[/tex], 其中[tex=9.357x3.643]r+tiAx6ClSaeP7cZbqpjmSQknJTvSyjmMn9KQrSttYf3zIfQ34uJf77prkHVmwBtUg1sQm/L+OX93K1V8lyVP6AnIkBa61KybF7Ps1O0+BW8dQxffy6Y25XUk5WfKhz3[/tex], [tex=4.786x3.5]t4TU5HQAVYrwy1dmvaCPG6gR9A0QcoABryDcNsMl4hWdCUY/tB7stPt/A+U6KTtsxs0wap+GUSbNmlzM8f2VIg==[/tex]。
求矩阵方程[tex=4.786x1.143]H9S8z2blJXaVphQETw95Fg==[/tex],其中[tex=9.357x3.643]QN0fTQbn6M33pU3gx/S2sskwPlrKAzoJ8mdYiTYC7tGO8szMd8p+2cNkEYkSMjdsANbknV+iJQh+J809zadp79g509gaMWeT6/svoAyzdUJEeD0/oHbgF3bAj/jVoWDM[/tex],[tex=7.071x3.643]DgXZT9CtCPAglTYwc4pEdaW9CmkkN7KSp7oXBK1jNeVVp3uIDYR9ryBYepwcyLDiivkA6raYMPp/oSHjfyBBw3StMI4KYC8c8tgVzNWxNFc=[/tex]。
求矩阵方程[tex=4.786x1.143]H9S8z2blJXaVphQETw95Fg==[/tex],其中[tex=9.357x3.643]QN0fTQbn6M33pU3gx/S2sskwPlrKAzoJ8mdYiTYC7tGO8szMd8p+2cNkEYkSMjdsANbknV+iJQh+J809zadp79g509gaMWeT6/svoAyzdUJEeD0/oHbgF3bAj/jVoWDM[/tex],[tex=7.071x3.643]DgXZT9CtCPAglTYwc4pEdaW9CmkkN7KSp7oXBK1jNeVVp3uIDYR9ryBYepwcyLDiivkA6raYMPp/oSHjfyBBw3StMI4KYC8c8tgVzNWxNFc=[/tex]。
解下列矩阵方程:[tex=4.786x1.143]SBrLCVZb0oIRk0NSteMVIg==[/tex], 其中[tex=9.357x3.643]QN0fTQbn6M33pU3gx/S2sskwPlrKAzoJ8mdYiTYC7tGO8szMd8p+2cNkEYkSMjdsANbknV+iJQh+J809zadp79g509gaMWeT6/svoAyzdUJEeD0/oHbgF3bAj/jVoWDM[/tex], [tex=7.071x3.643]DgXZT9CtCPAglTYwc4pEdTYIay0w+N644riaOQUVnBefFJCJvM3AhWpg9OHZYI3VXkBhQERag/69moKfOrghzSp3wnxIh7EjbNliO65dRLk=[/tex]
解下列矩阵方程:[tex=4.786x1.143]SBrLCVZb0oIRk0NSteMVIg==[/tex], 其中[tex=9.357x3.643]QN0fTQbn6M33pU3gx/S2sskwPlrKAzoJ8mdYiTYC7tGO8szMd8p+2cNkEYkSMjdsANbknV+iJQh+J809zadp79g509gaMWeT6/svoAyzdUJEeD0/oHbgF3bAj/jVoWDM[/tex], [tex=7.071x3.643]DgXZT9CtCPAglTYwc4pEdTYIay0w+N644riaOQUVnBefFJCJvM3AhWpg9OHZYI3VXkBhQERag/69moKfOrghzSp3wnxIh7EjbNliO65dRLk=[/tex]
用初等变换求矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]的逆矩阵[tex=1.714x1.214]ehC1Fy05fIHTeRCJHyodYA==[/tex],其中[tex=9.357x3.643]QN0fTQbn6M33pU3gx/S2skBf9r/jVKLZ7SYtu+2BgAGoXeCNmbjLSv6XuoZHCLh1+PA4Fjxgf9uDW9pKd4Ni/gioTZCIDvRotEI3NYLBxRhOvfIfTEciMevgO3Ne8jbS[/tex]
用初等变换求矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]的逆矩阵[tex=1.714x1.214]ehC1Fy05fIHTeRCJHyodYA==[/tex],其中[tex=9.357x3.643]QN0fTQbn6M33pU3gx/S2skBf9r/jVKLZ7SYtu+2BgAGoXeCNmbjLSv6XuoZHCLh1+PA4Fjxgf9uDW9pKd4Ni/gioTZCIDvRotEI3NYLBxRhOvfIfTEciMevgO3Ne8jbS[/tex]
用可逆矩阵将下列实对称矩阵化为标准形,并写出可逆矩阵[tex=0.643x1.0]WUJ/JHItsc3Bqx1WYNJcrg==[/tex].[tex=9.357x3.643]S3L+t9IHwQ0z1v720J0jKw4uUvkItaeKluAmqLy9J7hFn/DIr8whRgAHAoBqNj6n64BJy9CkSGcTYlvR1NbKjL2OOF23nLnGjKymWKTH2oZr+CPf4vzFLrtCxxqnU8vo[/tex].
用可逆矩阵将下列实对称矩阵化为标准形,并写出可逆矩阵[tex=0.643x1.0]WUJ/JHItsc3Bqx1WYNJcrg==[/tex].[tex=9.357x3.643]S3L+t9IHwQ0z1v720J0jKw4uUvkItaeKluAmqLy9J7hFn/DIr8whRgAHAoBqNj6n64BJy9CkSGcTYlvR1NbKjL2OOF23nLnGjKymWKTH2oZr+CPf4vzFLrtCxxqnU8vo[/tex].
如果矩阵[tex=9.357x3.643]3BT1BgBZQ5uJXxD5dg+w25oxXRH9+KEjMiNSxk6AZG+PsFZwXRxPIBN6s44j902W5vNNmOjVBXquMCKEgf/BNJ5SSXfj6kONTH2cuTJkBPIBOYobCdzUTg1N8KvXoIB3[/tex]与对角矩阵相似,则写出相似对角矩阵[tex=0.929x1.0]tfHTq5YB6eq76zMfF9z56Q==[/tex] 及 [tex=0.786x1.0]6J6pLBwELDvuZYB9vl6pdg==[/tex].解:
如果矩阵[tex=9.357x3.643]3BT1BgBZQ5uJXxD5dg+w25oxXRH9+KEjMiNSxk6AZG+PsFZwXRxPIBN6s44j902W5vNNmOjVBXquMCKEgf/BNJ5SSXfj6kONTH2cuTJkBPIBOYobCdzUTg1N8KvXoIB3[/tex]与对角矩阵相似,则写出相似对角矩阵[tex=0.929x1.0]tfHTq5YB6eq76zMfF9z56Q==[/tex] 及 [tex=0.786x1.0]6J6pLBwELDvuZYB9vl6pdg==[/tex].解: