广东海洋大学 线性代数14-15（答案）
发布时间：2019-06-06 16:11:10
![](https://wkrtcs.bdimg.com/rtcs/image?w=92&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"92","h":"750.66666666667","dataType":"gif","c":"word/media/image1.png"})
《线性代数》课程试题
课程号： | 19221201 | √ | 考试 | □ | A卷 | √ | 闭卷 | ||||||||||
□ | 考查 | √ | B卷 | □ | 开卷 | ||||||||||||
p < class=' _1'> | 题 号 | 一 | 二 | 三 | 四 | 五 | 六 | 总分 | 阅卷教师 | ||||||||
p < class=' _1'> | 各题分数 | 10 | 10 | 20 | 20 | 20 | 20 | 100 | |||||||||
p < class=' _1'> | 实得分数 | ||||||||||||||||
一、（10分）已知向量组![](https://wkrtcs.bdimg.com/rtcs/image?w=61&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"61","h":"24","dataType":"png","c":"word/media/image2_1.png","imgOriW":1472,"imgOriH":576})
线性无关，证明线性无关
设![](https://wkrtcs.bdimg.com/rtcs/image?w=255&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"255","h":"24","dataType":"png","c":"word/media/image5_1.png","imgOriW":4392,"imgOriH":412})
二、（10分）![](https://wkrtcs.bdimg.com/rtcs/image?w=142&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"142","h":"74","dataType":"png","c":"word/media/image6_1.png","imgOriW":1891,"imgOriH":990})
![](https://wkrtcs.bdimg.com/rtcs/image?w=389&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"389","h":"74","dataType":"png","c":"word/media/image7_1.png","imgOriW":3194,"imgOriH":613})
![](https://wkrtcs.bdimg.com/rtcs/image?w=173&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"173","h":"74","dataType":"png","c":"word/media/image8_1.png","imgOriW":2095,"imgOriH":903})
三、（20分）求![](https://wkrtcs.bdimg.com/rtcs/image?w=182&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"182","h":"74","dataType":"png","c":"word/media/image9_1.png","imgOriW":2154,"imgOriH":880})
的一个基础解系
![](https://wkrtcs.bdimg.com/rtcs/image?w=266&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"266","h":"74","dataType":"png","c":"word/media/image10_1.png","imgOriW":2625,"imgOriH":735})
，
![](https://wkrtcs.bdimg.com/rtcs/image?w=290&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"290","h":"122","dataType":"png","c":"word/media/image11_1.png","imgOriW":2160,"imgOriH":912})
四、（20分）求向量组
![](https://wkrtcs.bdimg.com/rtcs/image?w=433&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"433","h":"25","dataType":"png","c":"word/media/image12_1.png","imgOriW":5691,"imgOriH":330})
的秩和一个极大线性无关组，并把其他向量用该极大无关组线性表出
![](https://wkrtcs.bdimg.com/rtcs/image?w=371&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"371","h":"96","dataType":"png","c":"word/media/image13_1.png","imgOriW":2762,"imgOriH":713})
![](https://wkrtcs.bdimg.com/rtcs/image?w=49&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"49","h":"24","dataType":"png","c":"word/media/image14_1.png","imgOriW":1184,"imgOriH":576})
构成极大线性无关组，且
五、（20分）求矩阵X，使AX=A+X，其中![](https://wkrtcs.bdimg.com/rtcs/image?w=101&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"101","h":"74","dataType":"png","c":"word/media/image16_1.png","imgOriW":1578,"imgOriH":1162})
变为
![](https://wkrtcs.bdimg.com/rtcs/image?w=78&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"78","h":"26","dataType":"png","c":"word/media/image17_1.png","imgOriW":1888,"imgOriH":640})
![](https://wkrtcs.bdimg.com/rtcs/image?w=377&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"377","h":"149","dataType":"png","c":"word/media/image18_1.png","imgOriW":2245,"imgOriH":888})
6、（20分）1.验证（14分）
![](https://wkrtcs.bdimg.com/rtcs/image?w=509&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"509","h":"93","dataType":"png","c":"word/media/image19_1.png","imgOriW":3306,"imgOriH":603})
426×-40=-17040
2.填空（6分）
线性方程组![](https://wkrtcs.bdimg.com/rtcs/image?w=46&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"46","h":"18","dataType":"png","c":"word/media/image20_1.png","imgOriW":1120,"imgOriH":448})
有唯一解的充要条件是
向量组![](https://wkrtcs.bdimg.com/rtcs/image?w=97&md5sum=157cef1f5840915de37d06987ffb1121&sign=5efaa8d1e5&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=100&ipr={"t":"img","w":"97","h":"26","dataType":"png","c":"word/media/image22_1.png","imgOriW":2336,"imgOriH":640})
线性无关的充要条件是
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