《高中數(shù)學(xué) 第四講 變換的不變量與矩陣的特征向量 4.2 特征向量的應(yīng)用課件 新人教A版選修42》由會(huì)員分享，可在線閱讀，更多相關(guān)《高中數(shù)學(xué) 第四講 變換的不變量與矩陣的特征向量 4.2 特征向量的應(yīng)用課件 新人教A版選修42（26頁(yè)珍藏版）》請(qǐng)?jiān)谘b配圖網(wǎng)上搜索。
1、二二特征向量的應(yīng)用特征向量的應(yīng)用MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TO
2、UXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理1.利用矩陣A的特征值、特征向量給出An的簡(jiǎn)單的表示,并能用它來(lái)解決問(wèn)題.2.會(huì)利用特征向量解決簡(jiǎn)單的實(shí)際問(wèn)題.MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHAN
3、G目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHO
4、NGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理121.An的簡(jiǎn)單表示設(shè)A是一個(gè)二階矩陣,是矩陣A的屬于特征值的任意一個(gè)特征向量,則An=n(nN*).名師點(diǎn)撥名師點(diǎn)撥由此可把矩陣的乘方轉(zhuǎn)為實(shí)數(shù)的乘方,比較簡(jiǎn)便.MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目
5、標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHO
6、NGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOH
7、ANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演
8、練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理122.性質(zhì)設(shè)1,2是二階矩陣A的兩個(gè)不同特征值,1,2是矩陣A的分別屬于特征值1,2的特征向量,對(duì)于任意的非零平面向量,設(shè)=t11+t22(其中t1,t2為實(shí)數(shù)),則對(duì)任意的正整數(shù)n
9、,有名師點(diǎn)撥名師點(diǎn)撥由于1和2是矩陣A的分別屬于特征值1,2的特征向量,所以1與2不共線,由平面向量的基本定理,知平面內(nèi)的任意一個(gè)非零向量都可以用1和2表示出來(lái),即存在兩個(gè)實(shí)數(shù)t1,t2使=t11+t22,也就是可以用特征向量表示出來(lái).MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOH
10、ANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演
11、練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAO
12、DAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIA
13、N隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理1.設(shè)二階矩陣A的兩個(gè)特征值1,2對(duì)應(yīng)的兩個(gè)特征向量分別為1,2,為二階矩陣A對(duì)應(yīng)的線性變換,為平面內(nèi)的任意一個(gè)向量,那么An(nN*)能否用1和2表示出來(lái)呢?剖析:因?yàn)?,2
14、是二階矩陣A的兩個(gè)特征向量,所以1,2不共線,則平面內(nèi)的任意一個(gè)向量就可以用1,2表示出來(lái),即存在實(shí)數(shù)t1,t2使得=t11+t22,A1=11,A2=22.所以 =A=A(t11+t22)=t1(A1)+t2(A2)=t111+t222,2=A2=A(A)=A(t111+t222)=t11(A1)+t22(A2)MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONG
15、NAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理2.求An的基本步驟是什
16、么?剖析:第一步:由特征向量的定義A=,求出特征值和相應(yīng)的特征向量;第二步:把向量改寫為用1和2表示,即=t11+t22;第三步:由性質(zhì)公式計(jì)算MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONG
17、NAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理題型一題型二MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAO
18、DAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨
19、堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理題型一題型二MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)
20、梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理題型一題型二反思反思利用特征值和特征向量的知識(shí),可以方便地計(jì)算多次變換的結(jié)果. MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理
21、MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYA
22、NLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理題型一題型二【例2】 當(dāng)兔子和狐貍處于同一棲息地時(shí),忽略其他因素,只考慮兔子數(shù)量和狐貍數(shù)量的相互影響,為了簡(jiǎn)便起見(jiàn),不妨做如下假設(shè):(1)由于自然繁殖,兔子數(shù)每年增長(zhǎng)10%,狐貍數(shù)每年減少15%;(2)由于狐貍吃兔子,兔子數(shù)每年減少狐貍數(shù)的0.15倍,狐貍數(shù)每年增加兔子數(shù)的0.1倍;(3)第n年時(shí),兔子數(shù)量用Rn表示,狐貍數(shù)量用Fn表示;(4)初始時(shí)刻(即第0年),兔子數(shù)量有R0=100只,狐貍數(shù)量有F0=30只.這樣,兔子和狐貍的生態(tài)模型為試用矩陣知識(shí)求出Rn,Fn關(guān)于n的關(guān)系式,并討論當(dāng)n越來(lái)越大時(shí),兔
23、子和狐貍的數(shù)量是否能達(dá)到一個(gè)穩(wěn)定的平衡狀態(tài)?MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIA
24、NLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理題型一題型二分析:根據(jù)已知條件首先要轉(zhuǎn)化為向量表示及其矩陣形式表示,其次求出矩陣的特征值及其特征向量,最后解答. MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIA
25、ODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN
26、隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理題型一題型二和Fn分別趨向常量210和140,即隨著時(shí)間的增加,兔子和狐貍的數(shù)量逐漸增加,當(dāng)時(shí)間充分長(zhǎng)后,兔子和狐貍的數(shù)量達(dá)到一個(gè)穩(wěn)定的平衡狀態(tài).MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)
27、航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理題型一題型二反思反思解決實(shí)際問(wèn)題時(shí),需要先從題目中提煉出信息,本題轉(zhuǎn)為矩陣表示,用矩陣及特征向量表示解答問(wèn)題.MUB
28、IAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLI
29、AN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12345MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI
30、知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12345MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析
31、SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISH
32、I SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12345MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TO
33、UXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12345MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJ
34、IAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DI
35、ANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12345MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONG
36、NAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12345MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAOD
37、AOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂
38、演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理123455.自然界生物種群的成長(zhǎng)受到多種條件因素的影響,比如出生率、死亡率、資源的可利用性以及競(jìng)爭(zhēng)、捕食者的獵殺乃至自然災(zāi)害等等.因此它們和周邊環(huán)境是一種既相生又相克的生存關(guān)系.但是如果沒(méi)有任何限制,種群也會(huì)泛濫成災(zāi).現(xiàn)假設(shè)兩個(gè)互相影響的種群X,Y隨時(shí)間段變化的數(shù)量分別為an,bn,并有關(guān)系式MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI
39、典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦Z
40、HISHI SHULI知識(shí)梳理12345MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHONGNAN JVJIAO重難聚焦ZHISHI SHULI知識(shí)梳理12345
高中數(shù)學(xué) 第四講 變換的不變量與矩陣的特征向量 4.2 特征向量的應(yīng)用課件 新人教A版選修42
