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一星新手會員
2010-12-12 11:11#1
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 ] -
VIP會員
2010-12-12 21:56#2
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 ] -
VIP會員
2010-12-12 22:38#3
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 -
一星新手會員
2010-12-12 22:59#4
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... -
VIP會員
2010-12-12 23:08#5
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 ] -
一星新手會員
2010-12-12 23:18#6
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... -
VIP會員
2010-12-12 23:19#7
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 ] -
一星新手會員
2010-12-12 23:22#8
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...:ro03:
[ 本帖最後由 PinkyPYC 於 10-12-12 11:24 PM 編輯 ] -
版主
2010-12-13 14:02#9
4) 計上來超簡單。
1) 之前我還懂矩陣，但是忘剩了行列式。:smilie_O_o: -
一星新手會員
2010-12-15 22:51#10
謝謝你們的熱心幫忙，小女子真是感激流涕﹗﹗﹗:ro02: