報日僑華
四期星日十二月三年九六九一座公年八十五國民華中
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育華僑華
[1 Definition of matricas
上
文中學會考
考試題預習
A rectangular array of real numbers is called a matrix. It is important to notice that a matrix does not have a numerical value, but is only a collection of numbers arranged in a rectangular tabla. Mtrices are denoted by capital letters A, B, C and so on. Some examples of matrices are the following:
0-1
現代數學科
(二十)
李義
MODERN HATHEMATICS (20).
Solutione of the exercises assigned. Last week
(3): Prove that the modular: arithmetic mod 3 undar
addition is isomorphic to the group whose elements are the permutations
1.2
₤1.2.31 HP(312)
71.2
under the operation "followed by n, denoted by lion
Solution:
Addition table of arith- mod 3.
won table ar {e, p, ai y
The one-one correspondence between their
●lements is given as follow.
Order of a mat
A matrix with a row and n columns is said to be a matrix of order a x n. This means that the order
a matrix is given by stating first the number of rowa then the number of columns in the matrix. This the orders of matrices given in section 1 are respectively 2 x 3, 2 x 2, 4 x 1, and 1 × 3.
If a matrix has only one column, it is called ■ } column matrix; and if a matrix has only one row, it is called a row matrix. Thus example (3) is a colum mrix and example (4) is a row matrix. If the number of rows is the same as the number of columns, san the second example above, it is called a square
Given two linear equations in two variables; san form a square matrix with its coefficients. Example: Givan 3x-2y7 and I 33-4, the coefficients of x and y form a squa. 378
Matrix (33)
When we are speaking a square intrix of nex order, we often refer to its order as n rather than; nin. Thus the matrix of the coefficients of the two equations above has the order 2.
Bolution?
32
311 42-3
and
(2)Form a matrix of order 3 x 3 auch that adj = 0.
rifj and aid -1f1-1
Solution : Let the matrix be
1; and all the other entri
Thus the matriz becoMISS
(3) Form a matrix of order 4 x 2 auch that asy
21-4. Solution:
Let the strix-ba
x2
3
Henne their operations are "preserved."
(2) Prove that the set (2,4,6,8} under multiplication
mod 10 is isomorphic to the set {1,3,7,9} under multiplication mod 10.
Solution:
Tables of multiplications
The one-to-one correspondance between the
ia given as below,
3. Notations of matrices
·Capital letters are often used to denote general matrices, The entries in a matrix are of denoted by amall letters with subscripts. Thus, may. represent a matrix h of order 3 x 3 by
11 12
#21 22 23 and a matrix B of order 3x4 by 031 *32 033/
#22023
D32
in general, aij means that it is the entry in the ith row and th colum. Thus #32 is the entry in the third row and second column, and a13 As the entry in the first row and third column. The notation for a matrix may be also abbreviated as follows)
Am (a13), and B- (b1j)
(a1) 3 x 3
Equality of two matrices
Two matrices of the same order are said to be @quel if and only if their corresponding elements are equal. Examples+
Hence
(4) How many entries are there in a 4 x 5 matrix?
A matrix? In auxnatrix? Solution: Inaux5 matrix, there are 5. entries in each row, and there are 4 rows. Therefore there are 4 x 5 or 20 entries in a 4 x 5 matrix, Similarly, there are 3 x 4 or 12 entries in 3 x 4 matrix, and there are m x n entreia în am x`n matrix.
(5) Solve: (§ ~ ~ ) − ( 1 )
Solution::
Since the tuo matricea are equal and they are of the same order 2 x 13 the corresponding entries are equal; hence
2:
(6) If A - B and B-C, what would you say about
8 and C7 Axplain Solution:
x 8
and so on. These show that
and d = 0.
((2) (132)-(334)
means that
the operatio
are #preservad", hence the two
sets are isomorphic under multiplisations
(【3】 Solve: x • 6 (mod 7).
Solution: (3 x 3) x 3 - 2 x 3 • 6; (5-x.
4 x 5 - 63. (6 x 6) 16 - 1 x 6. • Therefore x • 3, œr 5, or 6,
{(4) Barve 1x + 8. 3 imod 1).
Solution: 28
3 +36]
(5) What wḍll be the day of the week 17 days from now,
aastuẳng now is Thursday? Solutions 17 4 4 0 (mod ?】
The day will be Sunday
(6) What month of the year will be 37 months from no
Cassuming now is March?
37 • 3 • 4-(mod 12),
Thelfmonth
will be April
The transpose of a ma trix
Given a matrix A, the transpose of A, denotad
by A is formed by interchanging its rows and columns Examples!
than B
23 ;)
Notice that if A the wx matrix.
Porked examplas
(a)t A
Write the transpose
A. Name the entry.
Name the entry,
Since' A = Band B C then
big and bij ani; Therefore
= cyy (transitive property
Similarly, aqz - ¢12) #21
$22
922.
Therefore A= C (definition of equality of
matrices)
Exercises for the week
(1) Form a matrix of order 3 x 5 such that aij
213.
(2) Form a matrix of order 2 x ↳ such that ai) =)
(3) Solve the equations.
(4)
。。。
Find A15):
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港區考生名列前茅
張建、李錦標本人成卓越
根據做實可署昨
會學院考試中殊得極高 聽著深感興 「香港真光女生! 再至在倫敦城市與工形,並作示範明難多大,全校英文書法比賽,由 八潮拭)本池书生,價值之所撦,闡述睟盡,街立本英文官院,畢行 校东净和研發各組类品
,各組得换名次如下:
星期三)前公佈之疗法 集體捐血
,在半院去年五月,
及六月舉行之考試中,
一港生獲得两現首獎。
日推九
三十集勷爲
|院之灣民爲大英聯邦九人,爲紅十Ó會 各地所保熙之冢門按衡遭血晝點,於本月十四 行此等考試之拙戚越畫」之精神,均備加讚許。),(二)迪斯製造 煤氣,電力,產業,木藝校辦理。校何中中 工鱀如下:.. *圈工荣泰院露 树各該生此稚見勇限公司八廠址香港鱈魚 工以至造船等等。.校長及紅魚主理人員,中國 有冇 切技術部門,由紡織,,由紅十字會派前往,行新俐峰徒訓練之三忠 考試,考試料官包一日自黏性爲該會獻血连被中先生現推 徐教城市與工展會中第十八齡以上學生一康紀濘,二名案淑芬‧ 代郵
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直升機動 臨香港教育問題
·潮州公邀請
可做有公能之招事 超不脚
器,深佈止多,缀校學可學
史者外了研來感
豬/李年制的
發瞧不设者在來度
因是難有
邀請竪道培中英文書院,它是有些讓碰的,那就是病苦枢蛋的私校與
新 校中集部举行海實時,,旁觀者潛」,這是中國人盡皆知的一句古话, 座談與演講,十七日 可發質外,對他們有沒有一點好嗎,『當局送 有各種對比賽及學術做,除了我明激實生局對擊宜就看問題,並將她 九潮州公學,任學期均有深入研究,眠是注意統計數字而已。請問這樣 〔港)安街 公佈出來。這不難明瞭,政府對這一問題,並沒 容宜燕講明通吃多,而尖學者更超過此數的矛煸現象,制止目
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理了够的夹入天循著
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注意賽點,及朗新一期藏了(席)