电大本科工程数学复习资料期末复习重点资料考试小抄

电大工程数学期末复习资料考试小抄 一、 线性代数 1、 矩阵的初等行变换：1）两行互换，2）某一行乘以一个非零常数，3）某一行的K倍加到另一行。

2、 阶梯型矩阵：1）全为0的行写在最下面，2）首非零元的列标随行标的增大而增大。如 3、 行简化阶梯型矩阵：满足下列条件的阶梯型矩阵：1）首非零元全为1，2）首非零元所在列其余元素全为0。如：
4、 求矩阵A的秩：A阶梯型矩阵。阶梯型矩阵非零行的行数既为矩阵A的秩即r(A) 例：
设矩阵，求矩阵的秩． 解：用初等行变换将矩阵化为阶梯形 由此可知矩阵的秩为2．　　　　 5、 求矩阵方程AX=B：（A B）(I X)或X=B 求矩阵A的逆矩阵：（A I）（I ） 1. 例：设矩阵A=,B=,求AB. 或解矩阵方程AX=B 解：（AB）= →→ ∴＝ 例：设矩阵，求：
解：
所以 ． 6 、n元线性方程组解的判定 1）AX=b ：r(A b)=r(A)时，方程组有解 r(Ab)≠r(A)时，方程组无解 AX=0：方程组一定有解 2）求齐次线性方程组AX=0的基础解系：将方程组中的自由未知量分别取（k，0，0）,(0,k,0),(0,0,k)形式所得到的解向量 3）求AX=0的一般解和全部解：
求AX=b的一般解和全部解：
例：设齐次线性方程组的系数矩阵经过初等行变换，得 求此齐次线性方程组的一个基础解系和通解． 解：
因为 得一般解：
（其中是自由元） 令，得；

令，得． 所以，是方程组的一个基础解系． 方程组的通解为：，其中是任意常数． 例：2.线性方程组的全部解 解：（A b）=→→→方程组的一般解将常数项视为零，取得 相应齐次方程组的一个基础解系，取原方程组的一个特解故方程组的全部解 X=+C 例：当取何值时，线性方程组 有解，在有解的情况下求方程组的全部解． 解：将方程组的增广矩阵化为阶梯形 　　　　　 由此可知当时，方程组无解。当时，方程组有解。　　 　　此时齐次方程组化为 　　　　 　 分别令及，得齐次方程组的一个基础解系 　　　　　 令，得非齐次方程组的一个特解 　　　　　 由此得原方程组的全部解为 　　　　　　（其中为任意常数）　 二、 概率部分　 1、假设为两事件，已知，求． 解：
2、正态分布X～ , ,P(X>b)=1-P（X<b）=1- 例：.设X～N(2,9),试求（1）P(X<11);(2)P（5<X<8）.（已知Φ（1）=0.8413， Φ（2）=0.9772，Φ（3）=0.9987） 解：P(X<11)=Φ()=Φ(3)=0.9987 P(5<X<8)=Φ()-Φ()=Φ(2)-Φ(1)=0.1359 3、估计区间和假设检验：对于正态分布N（ 1）方差已知：统计量U=，其中 置信区间：[,假设检验：若，则假设 成立 2）方差未知：统计量T= ， 置信区间：[,假设检验：若 ，则假设 例：. 某车间生产滚珠，已知滚珠直径服从正态分布．今从一批产品里随机取出9个，测得直径平均值为15.1mm，若已知这批滚珠直径的方差为，试找出滚珠直径均值的置信度为0.95的置信区间． 解：由于已知，故选取样本函数 　　　　　　　 已知，经计算得 　　　　　　　　 滚珠直径均值的置信度为0.95的置信区间为，又由已知条件，故此置信区间为　　 例：对某一距离进行4次独立测量，得到的数据为（单位：米）：
15.51, 15.47, 15.50, 15.52 由此计算出，已知测量无系统误差，求该距离的置信度为0.95的置信区间（测量值服从正态分布）． 解：由于未知， 已知，经计算得 　　　　　　　　　　　　　　　　　 该距离的置信度为0.95的置信区间为，又由已知条件，故此置信区间为。

例：.据资料分析，某厂生产的一批砖，其抗断强度X～N(32.5,1.21),今从这批砖中随机地抽取了9块，测得抗断强度（单位：kg/cm）的平均值为31.12，问这批砖的抗断强度是否合格（α=0.05，μ=1.96） 解：假设Ｈ：μ＝32.5 已知ｎ＝9，＝31.12　σ＝1.1 ===3.76>1.96 故认为这批砖的抗断强度不合格 例：某钢厂生产了一批管材，每根标准直径100mm,今对这批管材进行检验，随机取出9根，测得它们直径的平均值为99.9mm,样本标准差s=0.47,已知管材直径服从正态分布，问这批管材的质量是否合格（检验显著性水平α=0.05，） 解：假设H:μ=100 已知：n=9 s=0.47 =99.9 故认为这批管材的质量是合格的 请您删除一下内容，O(∩_∩)O谢谢！！！2015年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄请您删除一下内容，O(∩_∩)O谢谢！！！2015年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄The battle for young viewers CCTV is embracing Internet culture and working with independent producers on TV shows to woo audiences under 35. Han Bing bin reports. After charming audiences with his warm smile for 14 years, China Central Television host Li Jiaming recently found himself targeted by a group of young netizens unhappy with his style. The complaints came after Li hosted the premiere of Rising Star on Oct 31. It is a singing competition show that originated in Israel. Many young netizens found his hosting style slow and boring and mocked it as “CCTV evening gala style“. They even initiated an online campaign to replace him. The 40-year-old host＇s reaction to the criticism was surprising. During the second episode, he jokingly called himself “the slow Jiaming“ and acted much younger, talking faster and louder. “It＇s like selling a product. When the customers file a complaint, you must change,“ says Li. “In the Internet age, you get feedback very quickly. These young people are so cute. When you＇re willing to change for them, they will quickly like you back.“ In order to win more young viewers, CCTV is relying on programs such as Rising Star to embrace Internet culture. In Rising Star, a studio audience and fans watching on television vote for their favorite singers in real time, using the instant-messaging app WeChat. Rising Star was designed to be a live broadcast, but the Chinese version isn＇t because of policy reasons. Still, WeChat votes by viewers at home are still a major factor in determining which contestants advance to the next round. In the show＇s latest episode, more than 6.5 million votes were cast via WeChat. “Now the competition among entertainment shows is very fierce. Audiences have more diverse needs. CCTV needs to embrace an open attitude, interact with young audiences and blend with the Internet,“ says Lyu Yitao, director of CCTV＇s entertainment channel. The producer of Rising Star, Enlight Media, says the program will have “a phenomenal effect“ given CCTV＇s audience base nationwide. “But it comes with a challenge,“ says Zhang Hang, chief producer of the program and CEO of Enlight Media＇s TV business. Unlike top-ranking provincial satellite channels such as Hunan TV, which have a large base of young fans thanks to a series of phenomenally popular entertainment and reality shows, CCTV productions are usually more conservative and serious, and thus have a much older audience base. “If we were to run this program on Hunan, we may attract twice as many viewers,“ says Zhang. “But since we didn＇t make it there, we now have to make the best out of the given conditions. And it means we have to make certain compromises.“ When the current season of Rising Star ends, Zhang says his company will conduct an overall evaluation of the program and make adjustments for future seasons. Although audience ratings haven＇t lived up to Zhang＇s expectations, he says the program has already helped CCTV attract more young people. According to Enlight Media, the number of people ages 15 to 35 who watched the first episode of Rising Star was 76 percent higher than the usual audience for CCTV entertainment productions. In order to attract young audiences, CCTV has been working with independent production companies. As one of CCTV＇s closest partners, Enlight Media has produced several entertainment and reality shows for the company＇s channels, including the Chinese version of The Biggest Loser on CCTV＇s business channel and an original teenager talent show Shaonian Zhongguo－qiang (Strong Young Chinese) on CCTV1. This year CCTV also licensed EE-Media, the producer of the popular Super Girl talent shows, to produce the talk show Hi! 2014, hosted by Taiwan pop star Harlem Yu and one of China＇s most popular TV stars Xie Na. The show is geared toward younger audiences. Canxing Productions, which rose to fame with the success of its Voice of China series on Zhejiang TV, also produced two talent shows for CCTV. One is an original production called Songs of China, which ended up as one of CCTV＇s most watched programs of 2014. The State Administration of Press, Publication, Radio, Film and Television announced earlier this year that, starting in 2015, only one music talent show can be aired nationwide during prime time each season, and there can be only one program based on foreign formats each year. However, domestic media report that such policies don＇t apply to CCTV, meaning it will become a highly desired platform by production companies. Wang Changtian, CEO of Enlight Media, confirmed to the Shanghai Securities News that its programs scheduled to air on CCTV next year, which include at least two reality shows, won＇t be affected. A kung fu-themed reality show, produced by Canxing, is also reportedly scheduled to run on CCTV next year. CCTV is “very active. The level of its acceptance of new ideas is even beyond my imagination,“ says Zhang Hang. “Our cooperation with CCTV will surely continue.“ When winter comes, nothing is more relaxing than a hot spring bath. For thousands of years, natural mineral-rich hot spring baths have also been used to relieve health ailments. The water found in natural hot springs contains a variety of different minerals, and the most common one is sulfur. It has a “rotten egg“ smell but is excellent for skin. The sulfur-containing water might be just what the doctor ordered when it comes to relieving pain, stress, itchy skin, arthritis and more. Hot springs resorts are thriving as biting cold winter arrives. Here we take a look at some of the best natural hot springs China has to offer.

相关热词搜索：