问题
单项选择题
二次型f(x1，x2，x3)=(x1+x2)2+(x2-x3)2+(x3+x1)2的秩为（）。
A.1
B.2
C.3
D.4
答案
参考答案：B
解析：
因为二次型
二次型矩阵
易见r(A)=2，所以二次型的秩为2．
本题的陷阱：注意
不是坐标变换，(因为行列式为0)，不要误以为秩是3．
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二次型f(x1，x2，x3)=(x1+x2)2+(x2-x3)2+(x3+x1)2的秩为（）。
A.1
B.2
C.3
D.4
参考答案：B
解析：
因为二次型
二次型矩阵
易见r(A)=2，所以二次型的秩为2．
本题的陷阱：注意
不是坐标变换，(因为行列式为0)，不要误以为秩是3．
A farmer had a cow. (奶牛) He 36 very good care of this cow and one day when it was ill. He was very 37 . He telephoned the vet（兽医）. “What’s the problem?”the vet 38 him when he arrived. “My cow is ill,”the farmer said.“I don’t know what’s the matter 39 her. She’s lying down and won’t 40 up. She won’t eat, and she’s making a strange 41 .” The vet looked at the cow. “She’s certainly ill.” he said, “and she needs to take some very strong 42 .” He took a bottle out of his box, and put two pills into his 43 . “Give her these,” he said. “The pills should make her 44 .” “ 45 should I give them to her?” the farmer asked. The vet gave him a 46 tube（管子）. “Put this 47 in her mouth, ”he said,“then put the pills 48 the tube and blow( 吹). That’ll make it.” The vet went away. The next day he came to the 49 again. The farmer was sitting outside his house and looked 50 . “How’s your cow?”the vet asked. “No change,”the 51 said. “and I’m feeling very well myself.” “Oh?”the vet said.“ 52 .” “I did 53 you said,”the farmer answered.“I put the tube in the cow’s mouth and then put two 54 in it.” “And?”the vet asked. “The cow 55 first,”the farmer said.
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