---
# System prepended metadata

title: 線性代數猜題
tags: [學業共筆]

---

## 課本習題

【1.1】1
【1.2】1, 3(a)(b)(d), 5, 7, 23, 25, 27.
【1.3】7
【1.4】15, 17, 21, 35, 37, 39
【1.5】1, 7(a)(b), 11, 13, 15, 17, 19, 23.
【1.6】1, 3, 9, 13, 15, 19.
【1.7】27, 39.
【1.8】17, 27, 37, 45.
【1.9】13 [(c)答案有誤], 15, 19, 23

【2.1】13, 25, 29, 31.
【2.2】3, 5, 7, 11, 13, 15, 17, 19, 21, 29.
【2.3】3, 5, 7, 9, 11, 17, 19, 25, 27, 29, 31, 33

【3.1】3, 9, 11, 19, 25.
【3.2】3, 9, 11, 17(a).
【3.3】1, 3, 9, 13, 15, 19, 21, 25, 27, 31, 35, 37.
【3.4】1, 5, 9, 13, 15.
【3.5】1, 7, 9, 11, 13, 15, 17, 19, 21, 27.

【4.1】1, 3, 5, 9, 13.
【4.2】1, 3, 5, 11, 13.
【4.3】1, 3, 5(a), 9,11(a)(b), 13(a), 17, 21. 
【4.4】3, 5, 7(a), 13, 15.
【4.5】1, 3, 5, 7, 9, 13, 15, 17, 27(b)(c).
【4.6】1, 3, 5, 13, 17.
【4.7】1, 3, 7, 9, 15, 17.
【4.8】1, 3, 5, 7, 9, 11, 13, 15, 17, 21, 25, 27.
【4.9】1, 3, 5, 7, 9, 13, 19, 23, 25, 29.	

【5.1】3, 7, 9, 13, 15, 27.
【5.2】3, 5, 7, 9, 13, 17, 19, 25, 33.

【6.1】1, 7, 9, 11, 13, 15, 17, 19, 25, 27, 29.
【6.2】1, 3, 5, 9, 11, 17, 21, 23, 25, 27.
【6.3】1, 3, 5, 7, 9, 11, 15, 19, 21, 23, 27, 29, 35, 37.

【8.1】1, 3, 5, 7, 13, 15, 17, 19, 21, 23, 25, 35.
【8.2】3, 5, 7, 11, 13, 17, 19, 23, 25, 27, 29, 31.
【8.3】3, 5, 11, 17.
【8.4】1, 3, 5, 7, 9, 13, 15, 21.


### 考前猜題(期中範圍)

【1.2】5, 23, 25
【1.5】11
【1.6】3
【1.8】27, 37, 45.
【1.9】13 [(c)答案有誤]

【2.1】13, 31.
【2.2】7, 11, 15, 21
【2.3】31, 33

【3.1】9, 19
【3.2】9, 11
【3.3】17, 25, 35, 37.
【3.5】1, 9, 11, 17

【4.2】11, 13.
【4.3】13(a), 17 

### 考前猜題(期末範圍)

待重新整理:

> 【4.4】3
> 【4.5】13, 15, 17
> 【4.6】1, 3
> 【4.7】1, 7, 15
> 【4.8】7, 9, 13, 17, 27.
> 【4.9】1, 9, 19,
> 
> 【5.1】7, 13, 27.
> 【5.2】5, 7, 13, 17
 
【6.1】1, 7, 9, 11, 13, 15, 17, 19, 25, 27

6.1重點: inner porduct基本的運算

【6.2】5, 11, 17, **25**, 27.

6.2重點: 判斷是否為orthogonal
1. inner porduct為0則為orthogonal
2. 計算矩陣null space

【6.3】1, 11, **19**, 21, **27**, 29, 35, **37**.

6.3重點: 求正投影，用Gram-Schmidt 求 orthogonal Basis
1. 先用Gram-Schmid求orthogonal Basis後，再求orthnormal Basis
2. 看清楚題目給的是什麼Basis
3. 看清楚題目要得是甚麼Basis

【8.1】1, 3, 5, 7, 13, 15, 17, **19**, 21, **23**, **25**

8.1重點: 計算T(),求kernel和range，rank和nulity
2. 範例23基本必考，我覺得會考TA: $R^n > R^m$的題型
3. 承上，range(T) = column space, ker(T) = null space
4. rank(T) = rank(A), nullity(T) = nullity(A)

【8.2】3, 5, **7**, 13, **19**, 23, 25, 27, 29, 31. (我感覺8.2不會考)

8.2重點: 確認是否為one-to-one, onto
1. nullity = 0，則kernel = {0}，為one-to-one
2. 如果column vector spans $R^n$或linearly independent 則為onto

【8.3】3, 5, **11**, 17.

8.3重點: 如果同時符合one-to-one和onto則為isomorphism
1. 如果為isomorphism，則可以inverse

【8.4】1, 3, **5**, **7**, 9, **13**, 15

8.4重點: 很難解釋，練就對了 



## 期末必考題型(總計11)


### 4.5(小考考過類似的)

對應習題: 15(講義沒有對應範例)

![image](https://hackmd.io/_uploads/Sy44Ka9HA.png)

答:
![image](https://hackmd.io/_uploads/H1Z6Ke2H0.png)


對應習題: 小考

![image](https://hackmd.io/_uploads/ryZrYaqSA.png)

### 4.6(知道就好)

![image](https://hackmd.io/_uploads/Hkudb09SC.png)

### 4.7(小考考過類似的)

![image](https://hackmd.io/_uploads/BkBCZC9rA.png)

對應習題: 7

![image](https://hackmd.io/_uploads/ByMqfAqSR.png)

答:
![image](https://hackmd.io/_uploads/ByRrClhr0.png)


對應習題: 小考

![image](https://hackmd.io/_uploads/ByLeM0cB0.png)


### 4.8


**以下都要會求:**
* column space
* row space(必考)
* null space(必考)

![image](https://hackmd.io/_uploads/rygaLmfoB0.png)

對應習題: 9

![image](https://hackmd.io/_uploads/B1IhUfsH0.png)

答:
![image](https://hackmd.io/_uploads/ryytfbhrA.png)

### 5.1

![image](https://hackmd.io/_uploads/HknfqzirR.png)

![image](https://hackmd.io/_uploads/SyxIqGjBR.png)

對應習題: 7

![image](https://hackmd.io/_uploads/ryOwsfjrA.png)

答:

![image](https://hackmd.io/_uploads/H15qUG3HA.png)


對應習題:小考

![image](https://hackmd.io/_uploads/SkFKsMoS0.png)

geometric multiplicity = dim(Eigen value)

### 5.2

![image](https://hackmd.io/_uploads/Hk-aoQirR.png)


![image](https://hackmd.io/_uploads/SJGRRzjHA.png)

![image](https://hackmd.io/_uploads/S1mkkQirA.png)

對應習題: 17

![image](https://hackmd.io/_uploads/Hy9DJQiS0.png)

答:
![image](https://hackmd.io/_uploads/r1EwOm3HR.png)
![image](https://hackmd.io/_uploads/S1N1oDpB0.png)


### 6.2

![image](https://hackmd.io/_uploads/r1TBDg9SC.png)

對應習題: 25

![image](https://hackmd.io/_uploads/HJAPDeqSA.png)

答: NO

### 6.3

![image](https://hackmd.io/_uploads/Hy7iDg5HC.png)

對應習題: 37

![image](https://hackmd.io/_uploads/r1oCPe5BA.png)

答:

![image](https://hackmd.io/_uploads/SJVpzE3S0.png)


### 8.1

對應習題: 25(講義沒有對應範例)

![image](https://hackmd.io/_uploads/HJDz-lqrC.png)

答:
![image](https://hackmd.io/_uploads/rkJ0ku3S0.png)


### 8.3

![image](https://hackmd.io/_uploads/HkUmXATHR.png)


對應習題: 11(講義沒有對應範例)

![image](https://hackmd.io/_uploads/ByzvfecHR.png)

答:

![image](https://hackmd.io/_uploads/SkbobOnSA.png)


### 8.4(都會考)

![image](https://hackmd.io/_uploads/SyVNXx9rC.png)

對應習題: 5

![image](https://hackmd.io/_uploads/rJFtHg9SC.png)

答:
![image](https://hackmd.io/_uploads/SkbFod2H0.png)



![image](https://hackmd.io/_uploads/H1JBQg5BA.png)

對應習題: 7

![image](https://hackmd.io/_uploads/BJplIg9HR.png)

答:
![image](https://hackmd.io/_uploads/rJqVQchS0.png)


![image](https://hackmd.io/_uploads/BksOQgcH0.png)

對應習題: 13

![image](https://hackmd.io/_uploads/HJwGSlqH0.png)

答:
![image](https://hackmd.io/_uploads/BkGNUqhHC.png)

