2026軍隊(duì)文職數(shù)學(xué)1筆試跟練12

1. 設(shè)是階方陣，為的伴隨矩陣，且，已知齊次線性方程組有

非零解，則非齊次線性方程組（   ）.  

A. 無(wú)解                                                   B. 有唯一解

C. 有無(wú)窮多組解                                    D. 無(wú)法判斷解的情況

2. 下面四個(gè)矩陣中，使成立的矩陣有（   ）個(gè).

①                                        ②

③                                  ④

A. 1                                                         B. 2

C. 3                                                         D. 4

3. 維向量空間的基，到基，的過(guò)渡矩陣為（   ）.

A.                                                B. 

C.                                              D. 

4. 設(shè)是3階方陣，將的第1行與第2行交換得，再把的第2行加到第3行得，則

滿足的可逆矩陣為（   ）.

A.                                          B. 

C.                                          D. 

5. 已知，是矩陣的屬于特征值3的特征向量，是矩陣的屬于特

征值1的線性無(wú)關(guān)的特征向量，則下列矩陣可以是矩陣的是（   ）.

①.                            ②.

③.                          ④.

A. ① ③                                                 B. ② ④

C. ② ③                                                 D. ① ②

1.答案：C.解析：本題綜合考查非齊次方程組解的理論.

因?yàn)辇R次線性方程組有非零解，所以，又因?yàn)?img height="21" src="data:image/wmf;base64,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" width="44" />，所以，得，所以，因此齊次線性方程組有無(wú)窮多組解.  

又，所以的個(gè)線性無(wú)關(guān)的列向量是的基礎(chǔ)解系，所以可由的個(gè)線性無(wú)關(guān)的列向量線性表示，即可由的個(gè)列向量線性表示，因此非齊次線性方程組有解，所以C正確.

2.答案：B.解析：本題考查矩陣的運(yùn)算.

要想使矩陣滿足，則需滿足.滿足題意的有①②，具體可見(jiàn)紅師教育出品的《戎易學(xué)題庫(kù)》數(shù)學(xué)一專業(yè).

3.答案：B.解析：本題考查向量空間下不同基之間的過(guò)渡矩陣.

因?yàn)?img height="42" src="data:image/wmf;base64,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" width="315" />所以.

4.答案：A.解析： 本題考查初等變換與初等矩陣的關(guān)系.

由于，即，所以，A正確.

5.答案：A.解析：本題綜合考查特征值與特征向量的性質(zhì).

顯然①正確；在②中，由于，所以②錯(cuò)誤；在③中，仍是的屬于特征值1的線性無(wú)關(guān)的特征向量，所以③正確；在④中，因?yàn)?img height="21" src="data:image/wmf;base64,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" width="45" />不是的特征向量，所以④錯(cuò)誤，答案為A.

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