| A1 B1 1 |
| A2 B2 1 |
| A3 B3 1 |
is area of triangle with vertex (A1,B1),(A2,B2),(A3,B3). it is 0 iff the triangle is degenerate, ie they are on the straight line.
+ / -檢視主題
由 bugzpodder 於 星期六 八月 30, 2003 9:22 am
由 E.T 於 星期一 七月 07, 2003 10:31 pm
o ... ic ..." n*n "
thx ~
thx ~
由 Raceleader 於 星期一 七月 07, 2003 10:23 pm
n*n的都有
由 E.T 於 星期一 七月 07, 2003 10:18 pm
行列式 is very fun ~
有4列的行列式 ?
有4列的行列式 ?
由 ---- 於 星期一 七月 07, 2003 10:13 pm
|x1 y1 z1|
|x2 y2 z2|
|x3 y3 z3|
=x1| y2 z2 | - x2|y1 z1| +x3|y1 z1|
| y3 z3 | |y3 z3| |y2 z2|
|x2 y2 z2|
|x3 y3 z3|
=x1| y2 z2 | - x2|y1 z1| +x3|y1 z1|
| y3 z3 | |y3 z3| |y2 z2|
由 Raceleader 於 星期一 七月 07, 2003 10:10 pm
由 Raceleader 於 星期一 七月 07, 2003 10:05 pm
try type x1 instead of x1, because so hard to read
由 --- 於 星期一 七月 07, 2003 9:59 pm
=a1*b2*c3+a2*b3*c1+a3*b1*c2-(a1*b3*c2+a2*b1*c3+a3*b2*c1)
由 kevin 於 星期一 七月 07, 2003 9:55 pm
|a1 a2 a3|
|b1 b2 b3|
|c1 c2 c3|
假設是這樣..
可以跟我怎麼用嗎?
ps.國一而已..
|b1 b2 b3|
|c1 c2 c3|
假設是這樣..
可以跟我怎麼用嗎?
ps.國一而已..
由 --- 於 星期一 七月 07, 2003 9:53 pm
高二課本有
由 kevin 於 星期一 七月 07, 2003 9:49 pm
3列的行列式怎麼用??
由 ---- 於 星期一 七月 07, 2003 9:48 pm
Meowth 寫到:Too boring. 其實這麼多公式,都是基本的廢話
but we have to learn it this yr
由 --- 於 星期一 七月 07, 2003 9:47 pm
Too boring. 其實這麼多公式,都是基本的廢話
由 ---- 於 星期一 七月 07, 2003 9:43 pm
suggestion:
1. pin them
2. Post them after making an image in computer, and upload it, will be prettier
1. pin them
2. Post them after making an image in computer, and upload it, will be prettier
由 --- 於 星期一 七月 07, 2003 9:21 pm
(**) 線ㄉ公式:
(1) Slope y-intercept form:
斜截式
y = m x + b, if m is finite.
(2) Two point form:
兩點式
(x-x1)(y2-y1) = (y-y1)(x2-x1).
(3) Point slope form:
點斜式
y - y1 = m(x-x1), if m is finite.
(4) Intercept form:
截距式
x/a + y/b = 1, if neither a nor b is zero.
(5) Normal form:
法向式
x cos(omega) + y sin(omega) = p.
(6) Parametric form:
參數式
x = x1 + t cos(alpha),
y = y1 + t sin(alpha),
where t is any real number.
(7) Point direction form:
點向式
(x-x1)/A = (y-y1)/B,
where (A,B) is the direction of the line and P1 lies on the line.
(8) General form:
一般式
A x + B y + C = 0,
where A, B, and C are real numbers, and not both A and B are zero.
(**) 點線距離:
The distance from Ax + By + C = 0 to P1 is
d = (Ax1+By1+C)/sqrt(A2+B2).
(**) 兩線交點:
If A1x + B1y + C1 = 0 and A2x + B2y + C2 = 0 are two lines, then their slopes are given by m1 = -A1/B1 and m2 = -A2/B2.
If they intersect, their intersection point has coordinates
x = (-C1B2+C2B1)/(A1B2-A2B1), y = (-A1C2+A2C1)/(A1B2-A2B1).
(**) 3 線共交點:
A1x + B1y + C1 = 0,
A2x + B2y + C2 = 0,
A3x + B3y + C3 = 0,
are concurrent (that is, all pass through a single point) if and only if the determinant
| A1 B1 C1 |
| A2 B2 C2 |= 0.
| A3 B3 C3 |
(1) Slope y-intercept form:
斜截式
y = m x + b, if m is finite.
(2) Two point form:
兩點式
(x-x1)(y2-y1) = (y-y1)(x2-x1).
(3) Point slope form:
點斜式
y - y1 = m(x-x1), if m is finite.
(4) Intercept form:
截距式
x/a + y/b = 1, if neither a nor b is zero.
(5) Normal form:
法向式
x cos(omega) + y sin(omega) = p.
(6) Parametric form:
參數式
x = x1 + t cos(alpha),
y = y1 + t sin(alpha),
where t is any real number.
(7) Point direction form:
點向式
(x-x1)/A = (y-y1)/B,
where (A,B) is the direction of the line and P1 lies on the line.
(8) General form:
一般式
A x + B y + C = 0,
where A, B, and C are real numbers, and not both A and B are zero.
(**) 點線距離:
The distance from Ax + By + C = 0 to P1 is
d = (Ax1+By1+C)/sqrt(A2+B2).
(**) 兩線交點:
If A1x + B1y + C1 = 0 and A2x + B2y + C2 = 0 are two lines, then their slopes are given by m1 = -A1/B1 and m2 = -A2/B2.
If they intersect, their intersection point has coordinates
x = (-C1B2+C2B1)/(A1B2-A2B1), y = (-A1C2+A2C1)/(A1B2-A2B1).
(**) 3 線共交點:
A1x + B1y + C1 = 0,
A2x + B2y + C2 = 0,
A3x + B3y + C3 = 0,
are concurrent (that is, all pass through a single point) if and only if the determinant
| A1 B1 C1 |
| A2 B2 C2 |= 0.
| A3 B3 C3 |
[教學]線
由 --- 於 星期一 七月 07, 2003 9:19 pm
三點(x1,y1), (x2,y2), (x3,y3) 共線
充要條件:
行列式
|x1 y1 1|
|x2 y2 1| = 0.
|x3 y3 1|
充要條件:
行列式
|x1 y1 1|
|x2 y2 1| = 0.
|x3 y3 1|