设[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]为三阶实对称矩阵,且满足条件[tex=5.643x1.286]1tHlUluSX8oE64v/crJgo+tFLM4jMuMB5O34QZwfZtI=[/tex],已知[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]的秩[tex=3.857x1.286]3BDBDM8rV5IvPy55msUb8l72RHRNPHAUuqULnEZ+ljY=[/tex]。(Ⅰ)求[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]的全部特征值;(Ⅱ)当[tex=0.571x1.286]pc/qlnA3cxu8Ag9jp3tYHQ==[/tex]为何值时,矩阵[tex=3.357x1.286]deqqOevvw1p7qMvpetA4kZUoEk23SV9ee+VksbkoDk4=[/tex]为正定矩阵,其中[tex=0.786x1.286]esgwf7UWeyPnizAgk3o6GQ==[/tex]为三阶单位矩阵。
举一反三
- 设 [tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex] 为3阶实对称矩阵, [tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex] 的秩为2,且[tex=14.071x4.214]oWHLmHU+pdEDpvQAl1/az2irZYCrD5n7tNBH0h60RZSRkfTyMbMBkWJdSOttONIz/aIpuB0DtzqN3xTrH5FVBFKkoJXOzqySt1tvYGkL8nUSpkZNcAKMbOAlAVv2kcmeYi+6tOdfVK4HPlO56RaXfQwFcsY1NpD3d9aKf9Ap169R9RP7pwAAI9lrlWeM6IV2kUfE+cegTA/apb491EeeaUNBXKdUyfhOIoUPF4JiNlE4d515R6xesLAEOKJSo8se[/tex](I)求 [tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex] 的所有特征值与特征向量。(II)求矩阵 [tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]。(本题满分11分)
- 设[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]为3阶实对称矩阵,[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]的秩为2,且[tex=5.071x4.786]BlMQKlsYZJNb/MjzLQFEj6z0kHatmM8W077c4diXLpJiyZcvF6V9jMa22V2RH6vWEohPJQa/X+lTxFZeW6FaOQ==[/tex][tex=5.071x4.786]p6bi/or+446t5BMkqScFrb1e5BrX/yRnk7V1YhPGvhz2G6QLgPVvANTZEMeITQYw[/tex](I)求[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]的所有特征值与特征向量。(II)求矩阵[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]。(本题满分11分)
- 设[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]是[tex=0.643x1.286]ZsZs11iKEvfmzDIurZth8g==[/tex]阶实对称矩阵,[tex=0.786x1.286]syhD1QeVJHJnBYGPyhK8Pg==[/tex]是[tex=0.643x1.286]ZsZs11iKEvfmzDIurZth8g==[/tex]阶可逆矩阵。已知[tex=0.643x1.286]ZsZs11iKEvfmzDIurZth8g==[/tex]维列向量[tex=0.643x1.286]vYiGJJ9TAtvnQmM1PsOB8g==[/tex]是[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]的属于特征值[tex=0.571x1.286]B2ovqsb3k1n+9dueLzQ98w==[/tex]的特征向量,则矩阵[tex=4.857x1.286]lZJhV6IiJ5ok3rVbUZKwGo6YCPEmluaQdieH9lRODSE=[/tex]属于特征值[tex=0.571x1.286]B2ovqsb3k1n+9dueLzQ98w==[/tex]的特征向量是 未知类型:{'options': ['[tex=2.5x1.286]A2WUyzWnDu2OjkNTEOlucKOX3NkHEMnewtfDkLbUV5s=[/tex]', '[tex=2.071x1.286]40HUoZ1VEEnst0rnaaiURZ7ppkQybD/bQrCWDJDoi6U=[/tex]', '[tex=1.429x1.286]athUT5Qd76rmMeyGusa1xoV6ZznXy2KTDA/W0VFZulY=[/tex]', '[tex=3.929x1.286]LABgAJdR++GM0f46k3Baq5caphLPLGDkYb6Cn4P+xYw=[/tex]'], 'type': 102}
- 设[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex],[tex=0.786x1.286]7xu/f2QGSkxbr3vOcRhylg==[/tex],[tex=0.857x1.286]vDXv5B1sq5mojGRzJQ1zhA==[/tex]均为[tex=0.643x1.286]ZsZs11iKEvfmzDIurZth8g==[/tex] 阶矩阵,则下列结论中不正确的是 未知类型:{'options': ['若[tex=4.143x1.0]9vAZrVBg6W+vWWqAqEUyYXoYPO92hhe/vIHBTZmKYLU=[/tex],\xa0则 [tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex],[tex=0.786x1.286]7xu/f2QGSkxbr3vOcRhylg==[/tex],[tex=0.857x1.286]vDXv5B1sq5mojGRzJQ1zhA==[/tex]都可逆', '若[tex=4.214x1.0]NgvK2f5s9ijGZYUL/TNj2r7LSbP1/skDwSc+9HFHL5c=[/tex],\xa0且[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]\xa0可逆,则\xa0[tex=2.5x1.0]5kRDcmzBykhTjCvKxOkAs0shoc0mZQR5zpGhUJy5DsA=[/tex]', '若[tex=4.214x1.0]NgvK2f5s9ijGZYUL/TNj2r7LSbP1/skDwSc+9HFHL5c=[/tex],\xa0且[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]可逆,则\xa0[tex=4.214x1.0]rh0TX4MN9zCcC33s0tu8Nx2GPfIYDx7fjowFvCmY0U+2b1yDursqyw5k9BH/Vj9m[/tex]', '若[tex=3.357x1.0]NgvK2f5s9ijGZYUL/TNj2ml0vSa6A5K035rdcMAZA/4=[/tex],\xa0且[tex=3.071x1.214]v9C5PoQbOZP04i1O/pmEezJ4QFAHarLJxhvCZi1Qpz8=[/tex],\xa0则[tex=2.5x1.0]5kRDcmzBykhTjCvKxOkAs5W3jGSADaIUTtwJxPI4NRo=[/tex]'], 'type': 102}
- 设[tex=0.643x1.286]ZsZs11iKEvfmzDIurZth8g==[/tex]维向量[tex=7.786x2.071]/sEjM6mEqcxCjSub5L8TWyNKtjSxFlPCYqM3Ar6VJ2ZUBzlz5NwqDaBbWM/qiW9e[/tex],[tex=2.429x1.071]EGmWl7zgapQWyJIlth9AMw==[/tex],[tex=0.786x1.286]esgwf7UWeyPnizAgk3o6GQ==[/tex]为[tex=0.643x1.286]ZsZs11iKEvfmzDIurZth8g==[/tex]阶单位矩阵,矩阵[tex=5.857x1.286]0v/phQ45uzIX2qymtVKzQwoLYFXY/umJcLAlObSFYK/XojlwNQ0/Jbjm3jH6F8/C[/tex],矩阵[tex=6.571x2.0]wZTMMTXlU9TeDWyoTnL8dM4mNEe8n6tRTsSS5zti68avCbyA8DcZImuN8yO8/OpP[/tex],其中[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]的逆矩阵为[tex=0.786x1.286]7xu/f2QGSkxbr3vOcRhylg==[/tex],则[tex=1.571x1.286]HKnp+uHPBk2bwxzOgbygNw==[/tex][input=type:blank,size:4][/input]。