| 选修4-2：矩阵与变换 求矩阵M=
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矩阵M的特征多项式为f(λ)=
=λ2-λ-6=（λ-3）（λ+2），…（2分）λ-2 -4 -1 λ+1
令f（λ）=0，得到M的特征值λ1=3，λ2=-2． …（4分）
当λ1=3时，联立
，解得x-4y=0x-4y=0 -x+4y=0
矩阵M的一个特征向量为
； …（7分）4 1
当λ2=-2时，联立
，解得x+y=0-4x-4y=0 -x-y=0
矩阵M的一个特征向量为
． …（10分）1 -1
| 完形填空。 | ||||
| Once there lived an old man in a town. He always 1 a lot of things, so his wife always had to say to him, "Remember this." One day he went on a long 2 alone. Before he went out, his wife said, "Now you have all these things. Take care of them." He went to the station, bought a ticket and got on the train with 3 . About an hour later, the conductor (乘务员) came to the old man and said, "Will you please 4 me your ticket?" The old man looked for his ticket in all his pockets, but he couldn't find it. He was 5 ."I can't find my ticket. I really bought a ticket 6 I got on the train," said the old man."I 7 you bought a ticket. All right. You don't have to buy another one," said the conductor. But he 8 looked worried and said, "You don't know 9 . If I can't find my ticket, I don't remember my 10 where I am going." | ||||
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