求助, 用Matrix method方式計算
3X+4X=22
2X+5X=24
如何用Matrix method計算
2012-09-08 2:08 am
回答 (2)
2012-09-09 12:16 am
✔ 最佳答案
3x+4y=222x+5y=24
│3 4 22 │×(-2/3)↓
│2 5 24 │ ←
│3 4 22 │
│0 7/3 28/3 │ ×3←
│3 4 22 │
│0 7 28 │×(1/7)←
│3 4 22 │ ←
│0 1 4 │ ×(-4)↑
│3 0 6 │×(1/3)←
│0 1 4 │
│1 0 2 │
│0 1 4 │
x+0=2
0+y=4
x=2,y=4
2012-09-08 2:25 am
A = ( 3 4 )
( 2 5 )
det A = | 3 4 | = 15 - 8 = 7
| 2 5 |
A tranpose = ( 3 2 )
( 4 5 )
adj A = ( 5 - 4 )
( - 2 3 )
so A inverse = (1/7)( 5 - 4 )
( -2 3 )
so ( x ) = (1/7)( 5 - 4 ) ( 22 )
( y ) ( -2 3 ) ( 24 )
( x ) = (1/7) ( 110 - 96 )
( y ) ( -44 + 72 )
= (1/7) (14 )
( 28 )
= ( 2 )
( 4 )
so x = 2 and y = 4.
( 2 5 )
det A = | 3 4 | = 15 - 8 = 7
| 2 5 |
A tranpose = ( 3 2 )
( 4 5 )
adj A = ( 5 - 4 )
( - 2 3 )
so A inverse = (1/7)( 5 - 4 )
( -2 3 )
so ( x ) = (1/7)( 5 - 4 ) ( 22 )
( y ) ( -2 3 ) ( 24 )
( x ) = (1/7) ( 110 - 96 )
( y ) ( -44 + 72 )
= (1/7) (14 )
( 28 )
= ( 2 )
( 4 )
so x = 2 and y = 4.
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