有幾條數學唔識做，請各位多多幫忙一下﹗﹗﹗

PinkyPYC

有幾條數學唔識做，身邊又冇人可以問到，眼見就來要交，有點兒想喊...請各位多多幫忙一下，在下不勝感激﹗﹗﹗

Q1. Given the following matrices:
A =1 2  , B = (4 1 2)  , C =1 0 4     and D =1
     3 1                              3 2 1                  2
                                        0 5 3                  2
Evaluate
(a) A2 , BC and BD.
(b) DB, CD and C2 .

Q2. Solve the following system of inhomogeneous linear equations:
4X3 + X4 = 1
2X1 + 2X2 – 2X3 + 5X4 = 1
5X1 + 5X2 -  X3 + 5X4 = 2

Q3. (a) Solve the following systems of linear equations:
x + y = 1
2x – y = 5
3x + 4y= 2
(b) Given the following systems of linear equations:
y + 2z = 1
x – 3z = 1
(k^2 - 4)z = k - 2
Find the values of k for which the system has (i) a unique solution,
(ii) infinitely many solutions, (iii) no solutions.

Q4. Find the value t for which the following system is consistent and solve the system for this value of t.
                                x + y = 2
                                x – y = 0
                                3x – y = t

[ 本帖最後由 PinkyPYC 於 10-12-12 11:38 PM 編輯 ]

Naozumi

第1題只係普通的matrix乘法運算,所以只做兩題示範一下,其他樓主要試一試




[ 本帖最後由 Naozumi 於 10-12-12 10:40 PM 編輯 ]

Naozumi

Q4
先solve
x + y = 2
x - y = 0

即 x = 1, y = 1,

咁個system要consistent,x = 1, y = 1就要satisfy 3x – y = t
所以 t = 3(1) - (1) = 2

我想問Q2有冇打錯data,計出黎的答案有d怪

PinkyPYC

Q2冇打錯呀...條題目係咁...
你可唔可以俾Q1個ans我？好讓我可以check下自己有冇計錯...
仲有Q3既part b你係點計架？我唔係好明呀...

Naozumi

Q3 個key point係(k^2 - 4)z = k - 2度因為原本個system係
y = 1 - 2z
x = 1 + 3z
(k^2 - 4)z = k - 2
所以只要(k^2 - 4)z = k - 2有unique solution/no solution/infinitely many solution就得

咁 k^2 - 4 唔係0,咁z得一個答案 (k - 2)/(k^2 - 4) ,
如果 k^2 - 4 = 0, k - 2 = 0 咁k^2 - 4)z = k - 2即係 0z = 0,所以有infinitely many solution



[ 本帖最後由 Naozumi 於 10-12-12 11:16 PM 編輯 ]

PinkyPYC

咁Q3有冇咩step去計有冇unique solution/no solution/infinitely many solution架？
如果照你post俾我既寫好怪怪地咁...

Naozumi

要好正統,咪用番gaussian elimination將個coefficient matrix用elementary row operation轉做echelon form

[ 本帖最後由 Naozumi 於 10-12-12 11:21 PM 編輯 ]

PinkyPYC

即係點計？我就係唔識計matrices﹑gaussian elimination...呢類既數...
偏偏呢份功課就係計呢類既數...

[ 本帖最後由 PinkyPYC 於 10-12-12 11:24 PM 編輯 ]

雪子秀

4) 計上來超簡單。

1) 之前我還懂矩陣，但是忘剩了行列式。

PinkyPYC

謝謝你們的熱心幫忙，小女子真是感激流涕﹗﹗﹗