在下列二次型中, 正惯性指数等于 2 的是 未知类型:{'options': ['[tex=13.786x1.571]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKAD1EpX2EG4iGqmx8WmWIijQ/1TBKOkYUR3PceE6jcAcuJWCFZNY7rgfvoZD8hjgnH6mnfX7xFxYsxbeC8J0MU/[/tex]', '[tex=20.0x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMgh6qDu0Esm2hn0XdQHhgVu9qtIccLZ4PooZnR82N9TbDifHftkucc0Q6jUSD/QldaNHWkbnhOWTFIHc8kOCmgQ==[/tex]', '[tex=12.786x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMrpG3Ol8X9Iuj7ckTZPEhiXRJE291fLQSXdrfPCxIyD0=[/tex]', '[tex=19.5x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMrpG3Ol8X9Iuj7ckTZPEhiZT9IGbyWQcJ4g2U4WKVdSafU4LRqNlmItRnMTLxj2I+ESRedIlCVJELqkZllvLTdw==[/tex]'], 'type': 102}
在下列二次型中, 正惯性指数等于 2 的是 未知类型:{'options': ['[tex=13.786x1.571]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKAD1EpX2EG4iGqmx8WmWIijQ/1TBKOkYUR3PceE6jcAcuJWCFZNY7rgfvoZD8hjgnH6mnfX7xFxYsxbeC8J0MU/[/tex]', '[tex=20.0x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMgh6qDu0Esm2hn0XdQHhgVu9qtIccLZ4PooZnR82N9TbDifHftkucc0Q6jUSD/QldaNHWkbnhOWTFIHc8kOCmgQ==[/tex]', '[tex=12.786x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMrpG3Ol8X9Iuj7ckTZPEhiXRJE291fLQSXdrfPCxIyD0=[/tex]', '[tex=19.5x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMrpG3Ol8X9Iuj7ckTZPEhiZT9IGbyWQcJ4g2U4WKVdSafU4LRqNlmItRnMTLxj2I+ESRedIlCVJELqkZllvLTdw==[/tex]'], 'type': 102}
在下列二次型中, 正惯性指数等于 2 的是 未知类型:{'options': ['[tex=13.786x1.571]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKAD1EpX2EG4iGqmx8WmWIijQ/1TBKOkYUR3PceE6jcAcuJWCFZNY7rgfvoZD8hjgnH6mnfX7xFxYsxbeC8J0MU/[/tex]', '[tex=20.0x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMgh6qDu0Esm2hn0XdQHhgVu9qtIccLZ4PooZnR82N9TbDifHftkucc0Q6jUSD/QldaNHWkbnhOWTFIHc8kOCmgQ==[/tex]', '[tex=12.786x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMrpG3Ol8X9Iuj7ckTZPEhiXRJE291fLQSXdrfPCxIyD0=[/tex]', '[tex=19.5x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMrpG3Ol8X9Iuj7ckTZPEhiZT9IGbyWQcJ4g2U4WKVdSafU4LRqNlmItRnMTLxj2I+ESRedIlCVJELqkZllvLTdw==[/tex]'], 'type': 102}
在下列二次型中, 正惯性指数等于 2 的是 未知类型:{'options': ['[tex=13.786x1.571]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKAD1EpX2EG4iGqmx8WmWIijQ/1TBKOkYUR3PceE6jcAcuJWCFZNY7rgfvoZD8hjgnH6mnfX7xFxYsxbeC8J0MU/[/tex]', '[tex=20.0x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMgh6qDu0Esm2hn0XdQHhgVu9qtIccLZ4PooZnR82N9TbDifHftkucc0Q6jUSD/QldaNHWkbnhOWTFIHc8kOCmgQ==[/tex]', '[tex=12.786x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMrpG3Ol8X9Iuj7ckTZPEhiXRJE291fLQSXdrfPCxIyD0=[/tex]', '[tex=19.5x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDxI5EU0Rj+WwqAYMSi5YHMrpG3Ol8X9Iuj7ckTZPEhiZT9IGbyWQcJ4g2U4WKVdSafU4LRqNlmItRnMTLxj2I+ESRedIlCVJELqkZllvLTdw==[/tex]'], 'type': 102}
设[tex=15.429x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtkhSnIVg0YM+RT9EoYtnIRIBBCDLMZrxexPB7Q92nwqaNObvRfNr6fYoOxxOOB5KeWi8dul/72Aa7meWWDOofJ[/tex][tex=15.286x1.357]w1jiwhN28M7EUOfAKymDSvWjp6tLsrVLtIXWni4H/yqeUDeR7tgFdBDMMUqDi4C8Axoj5KcGYhKgXHI1eMxvFT2yqz8JU0J5G6ZVzZeoKkcA99jh3wF1mYUl6jKO+z7UhchjGZybAgTgnzm/cBb3yQ==[/tex],且[tex=9.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTub7SnipdUJYMGMtGPDS5DqJ/Mr11NKCm+1NmpWlqOOpQ==[/tex]。证明,如果[tex=30.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtZaVO0g6AJVDgZVz9tirIxrXANZ1N7F66XV5ymKSTY8VFNq8H9/9aRjFWO8CF4ueq3kBqAdofeE9+YnzZaPwQxFmJfebIORvJBMC47hDrAFP9fnVIxxOGh2MINi5k61+sLzQM7CsSPQ5syjoyb+o593oXxP00P0RPpEZNZeWR7wevjE8W+alPvRRHHNxhkXhA=[/tex]则[tex=15.357x1.357]vvUfMWB7qhXreignZ7ucHuuF3Eo9DkR508wp+cFQ3Ib//UZiNfe3Fdu2MSfHozk0YGaQO+5BMYnL+LBTAu3JTVzuInnPVyN/THdsdSGWGzc1odjTMsA5roIg5wjj/7oc[/tex]。
设[tex=15.429x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtkhSnIVg0YM+RT9EoYtnIRIBBCDLMZrxexPB7Q92nwqaNObvRfNr6fYoOxxOOB5KeWi8dul/72Aa7meWWDOofJ[/tex][tex=15.286x1.357]w1jiwhN28M7EUOfAKymDSvWjp6tLsrVLtIXWni4H/yqeUDeR7tgFdBDMMUqDi4C8Axoj5KcGYhKgXHI1eMxvFT2yqz8JU0J5G6ZVzZeoKkcA99jh3wF1mYUl6jKO+z7UhchjGZybAgTgnzm/cBb3yQ==[/tex],且[tex=9.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTub7SnipdUJYMGMtGPDS5DqJ/Mr11NKCm+1NmpWlqOOpQ==[/tex]。证明,如果[tex=30.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtZaVO0g6AJVDgZVz9tirIxrXANZ1N7F66XV5ymKSTY8VFNq8H9/9aRjFWO8CF4ueq3kBqAdofeE9+YnzZaPwQxFmJfebIORvJBMC47hDrAFP9fnVIxxOGh2MINi5k61+sLzQM7CsSPQ5syjoyb+o593oXxP00P0RPpEZNZeWR7wevjE8W+alPvRRHHNxhkXhA=[/tex]则[tex=15.357x1.357]vvUfMWB7qhXreignZ7ucHuuF3Eo9DkR508wp+cFQ3Ib//UZiNfe3Fdu2MSfHozk0YGaQO+5BMYnL+LBTAu3JTVzuInnPVyN/THdsdSGWGzc1odjTMsA5roIg5wjj/7oc[/tex]。
设[tex=15.429x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtkhSnIVg0YM+RT9EoYtnIRIBBCDLMZrxexPB7Q92nwqaNObvRfNr6fYoOxxOOB5KeWi8dul/72Aa7meWWDOofJ[/tex][tex=15.286x1.357]w1jiwhN28M7EUOfAKymDSvWjp6tLsrVLtIXWni4H/yqeUDeR7tgFdBDMMUqDi4C8Axoj5KcGYhKgXHI1eMxvFT2yqz8JU0J5G6ZVzZeoKkcA99jh3wF1mYUl6jKO+z7UhchjGZybAgTgnzm/cBb3yQ==[/tex],且[tex=9.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTub7SnipdUJYMGMtGPDS5DqJ/Mr11NKCm+1NmpWlqOOpQ==[/tex]。证明,如果[tex=30.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtZaVO0g6AJVDgZVz9tirIxrXANZ1N7F66XV5ymKSTY8VFNq8H9/9aRjFWO8CF4ueq3kBqAdofeE9+YnzZaPwQxFmJfebIORvJBMC47hDrAFP9fnVIxxOGh2MINi5k61+sLzQM7CsSPQ5syjoyb+o593oXxP00P0RPpEZNZeWR7wevjE8W+alPvRRHHNxhkXhA=[/tex]则[tex=15.357x1.357]vvUfMWB7qhXreignZ7ucHuuF3Eo9DkR508wp+cFQ3Ib//UZiNfe3Fdu2MSfHozk0YGaQO+5BMYnL+LBTAu3JTVzuInnPVyN/THdsdSGWGzc1odjTMsA5roIg5wjj/7oc[/tex]。
设[tex=15.429x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtkhSnIVg0YM+RT9EoYtnIRIBBCDLMZrxexPB7Q92nwqaNObvRfNr6fYoOxxOOB5KeWi8dul/72Aa7meWWDOofJ[/tex][tex=15.286x1.357]w1jiwhN28M7EUOfAKymDSvWjp6tLsrVLtIXWni4H/yqeUDeR7tgFdBDMMUqDi4C8Axoj5KcGYhKgXHI1eMxvFT2yqz8JU0J5G6ZVzZeoKkcA99jh3wF1mYUl6jKO+z7UhchjGZybAgTgnzm/cBb3yQ==[/tex],且[tex=9.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTub7SnipdUJYMGMtGPDS5DqJ/Mr11NKCm+1NmpWlqOOpQ==[/tex]。证明,如果[tex=30.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtZaVO0g6AJVDgZVz9tirIxrXANZ1N7F66XV5ymKSTY8VFNq8H9/9aRjFWO8CF4ueq3kBqAdofeE9+YnzZaPwQxFmJfebIORvJBMC47hDrAFP9fnVIxxOGh2MINi5k61+sLzQM7CsSPQ5syjoyb+o593oXxP00P0RPpEZNZeWR7wevjE8W+alPvRRHHNxhkXhA=[/tex]则[tex=15.357x1.357]vvUfMWB7qhXreignZ7ucHuuF3Eo9DkR508wp+cFQ3Ib//UZiNfe3Fdu2MSfHozk0YGaQO+5BMYnL+LBTAu3JTVzuInnPVyN/THdsdSGWGzc1odjTMsA5roIg5wjj/7oc[/tex]。
求出 [tex=19.5x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKCsCQQs0kC5W8MRNDQYOdqMOUY3YzFfAg6pqV6HqP5U0FsSPwznyBbTjydSKtfDqzOXIM1u8ywh09b+D5whilglDFnGss2Mluv0EieYFSG/sQ==[/tex]的规范形.
求出 [tex=19.5x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKCsCQQs0kC5W8MRNDQYOdqMOUY3YzFfAg6pqV6HqP5U0FsSPwznyBbTjydSKtfDqzOXIM1u8ywh09b+D5whilglDFnGss2Mluv0EieYFSG/sQ==[/tex]的规范形.
判定以下二次型是不是正定二次型(需说明理由).[tex=33.286x1.5]CKlOGn/4oc+CIjd/NrEXYLzReNaNBndVcM3x5k1BscrWgyezPeeQrncRgogz9OwB19jbIiKErsZn5TwTU1J/guytuBEvid1x4qFc1T474a1NiR2cM2afWQyjonAS9bu9DgJctFHEnTgzrBft/D2v10sYpPkPV19+UueZglio9TMOxuyltR6lHB8zHb6uYn2rjHB0b/PbMYHIRTuKE8ijgQ==[/tex]
判定以下二次型是不是正定二次型(需说明理由).[tex=33.286x1.5]CKlOGn/4oc+CIjd/NrEXYLzReNaNBndVcM3x5k1BscrWgyezPeeQrncRgogz9OwB19jbIiKErsZn5TwTU1J/guytuBEvid1x4qFc1T474a1NiR2cM2afWQyjonAS9bu9DgJctFHEnTgzrBft/D2v10sYpPkPV19+UueZglio9TMOxuyltR6lHB8zHb6uYn2rjHB0b/PbMYHIRTuKE8ijgQ==[/tex]
用正交变换 法将下列二次型化为标准形,并写出所作的正交变换的矩阵:[tex=12.929x1.357]CKlOGn/4oc+CIjd/NrEXYLzReNaNBndVcM3x5k1BscqqBTNxm1O35m/m+o6M8ADkIFbIKHTGp+1f1trx2pVTi6GTbBb4dXJ6vkppKLfTt1Q=[/tex]
用正交变换 法将下列二次型化为标准形,并写出所作的正交变换的矩阵:[tex=12.929x1.357]CKlOGn/4oc+CIjd/NrEXYLzReNaNBndVcM3x5k1BscqqBTNxm1O35m/m+o6M8ADkIFbIKHTGp+1f1trx2pVTi6GTbBb4dXJ6vkppKLfTt1Q=[/tex]
若实对称矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]与矩阵[tex=7.786x3.5]opqi7S5YyIUs5JQiNQr2vJ+2NLxb3mgUQ8cog+A0uO2//e5NPySzN4MJqurCOu3PQ4sjWYw/glS+VBTLQqFwyMVpffnUZyoaZcZ5F5P77ABiD39SaSACFqXYjbIOp8DA[/tex]合同,求二次型[tex=8.643x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKANXOvDx2kgU1OQ41Fvjv7S4wy3sQ/s+4w1gaNWiYzEfA==[/tex]的规范形.
若实对称矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]与矩阵[tex=7.786x3.5]opqi7S5YyIUs5JQiNQr2vJ+2NLxb3mgUQ8cog+A0uO2//e5NPySzN4MJqurCOu3PQ4sjWYw/glS+VBTLQqFwyMVpffnUZyoaZcZ5F5P77ABiD39SaSACFqXYjbIOp8DA[/tex]合同,求二次型[tex=8.643x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKANXOvDx2kgU1OQ41Fvjv7S4wy3sQ/s+4w1gaNWiYzEfA==[/tex]的规范形.
设二次型[tex=8.643x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKANXOvDx2kgU1OQ41Fvjv7S4wy3sQ/s+4w1gaNWiYzEfA==[/tex]经正交变换化为标准形[tex=3.643x1.5]7V9lHlsR3o+lQ4ZvsgESPk415mbTzLbIcA4VmB6X2UA=[/tex],求[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]的特征值及[tex=1.143x1.357]m3nRCpZgU5gVkSZji8k5kw==[/tex].
设二次型[tex=8.643x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKANXOvDx2kgU1OQ41Fvjv7S4wy3sQ/s+4w1gaNWiYzEfA==[/tex]经正交变换化为标准形[tex=3.643x1.5]7V9lHlsR3o+lQ4ZvsgESPk415mbTzLbIcA4VmB6X2UA=[/tex],求[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]的特征值及[tex=1.143x1.357]m3nRCpZgU5gVkSZji8k5kw==[/tex].
已知实二次型[tex=8.429x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDKCw4XacjR6Wkq7aCfgBox[/tex]经正交变换[tex=2.857x1.0]NGl8c6nTOCjuPJKs2cOxRw==[/tex]可化为标准形[tex=5.571x1.5]BxX+JKGKByN8807bHgu+T1pktokv0l3dVZx8FO3ro+VWSdtzbyfx30MD7Apuy3Zt[/tex],则矩阵[tex=4.0x1.357]EBNDcMm1xMDWg08FZWWY1Q==[/tex][input=type:blank,size:6][/input].
已知实二次型[tex=8.429x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDKCw4XacjR6Wkq7aCfgBox[/tex]经正交变换[tex=2.857x1.0]NGl8c6nTOCjuPJKs2cOxRw==[/tex]可化为标准形[tex=5.571x1.5]BxX+JKGKByN8807bHgu+T1pktokv0l3dVZx8FO3ro+VWSdtzbyfx30MD7Apuy3Zt[/tex],则矩阵[tex=4.0x1.357]EBNDcMm1xMDWg08FZWWY1Q==[/tex][input=type:blank,size:6][/input].