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¨Ò¡G¸Ñ¤èµ{²Õ
3x+4y+z = 10
x+3y+z = 7
2x-3y+2z = 5
¶¶§Ç¿é¤J
3 EXE 4 EXE 1
EXE 10 EXE
1 EXE 3 EXE 1 EXE 7 EXE
2 EXE -3 EXE 2 EXE 5 EXE
Åã¥Ü 18 (
¤èµ{²Õ¦æ¦C¦¡ Determinant ªº¼ÆÈ¡A¦p¾A¥Î )
¦A«ö EXE Åã¥Ü 1 ( x
ªº¼ÆÈ )
¦A«ö EXE Åã¥Ü 1 ( y
ªº¼ÆÈ )
¦A«ö EXE Åã¥Ü 3 ( z
ªº¼ÆÈ )
Áp¥ß¤T¤¸¤@¦¸¤èµ{(general sollution)¨Ï¥Î¤èªk
¨Ò¡G¸Ñ¤èµ{²Õ
3x+2y+z
= 4
7x+6y+5z
= 8
11x+10y+9z
= 12
¶¶§Ç¿é¤J
3 EXE 2 EXE 1 EXE 4 EXE
7 EXE 6 EXE 5 EXE 8 EXE
11 EXE 10 EXE 9 EXE 12 EXE
Åã¥Ü 3 (
y ªº¸Ñ¡A±`¼Æ¶µ )
¦A«ö EXE Åã¥Ü -2 (
z ªº¸Ñ¡A±`¼Æ¶µ )
¦A«ö EXE Åã¥Ü -2 (
y ªº¸Ñ¡At
ªº«Y¼Æ )
¦A«ö EXE Åã¥Ü 1 (
z ªº¸Ñ¡At
ªº«Y¼Æ )
¥ç§Y¬O»¡ x = t ¡F y = -2t+3 ¡F z = t-2 ( x = t ¬O¹w³] )
°²³]¤èµ{²Õ¬O
A1x+B1y+C1z
= D1
A2x+B2y+C2z = D2
A3x+B3y+C3z = D3
¦pªGµ{¦¡¥X²{¿ù»~
Math ERROR¡A¥i¯à¬O
(1) ¤£²Å¦X¨Ï¥Î±ø¥ó
(2) ¦æ¦C¦¡ªº¼ÆÈ¬° 0
µ{¦¡°õ¦æ§¹¦¨«á¡A«ö
RCL A¡BRCL B¡BRCL C
¤À§O·|Åã¥Ü x¡By ¤Î
z ªº¼ÆÈ¡A
¦Ó RCL D «h·|Åã¥Ü¤èµ{²Õ¦æ¦C¦¡
Determinant ªº¼ÆÈ¡C
---------------------------------------------------------------------------------------------------
Áp¥ß¤G¤¸¤@¦¸¤èµ{¨Ï¥Î¤èªk
¨Ò¡G ¸Ñ¤èµ{²Õ
3x+4y = 10
x+3y = 5
¶¶§Ç¿é¤J
0 EXE 3 EXE 4 EXE 10 EXE ( ²Ä¤@Ó¤èµ{¡A²Ä¤@ӼƦr 0 ¬°¥²¶·
)
0 EXE 1 EXE 3 EXE 5 EXE ( ²Ä¤GÓ¤èµ{¡A²Ä¤@ӼƦr 0 ¬°¥²¶·
)
Åã¥Ü 2 ( x ªº¼ÆÈ )
¦A«ö EXE Åã¥Ü 1 ( y
ªº¼ÆÈ )
¦A«ö EXE Åã¥Ü 5 ( ¤èµ{²Õ¦æ¦C¦¡ Determinant ªº¼ÆÈ¡A¦p¾A¥Î )
°²³]¤èµ{²Õ¬O
B1x+C1y
= D1
B2x+C2y = D2
¦pªGµ{¦¡¥X²{¿ù»~
Math ERROR¡A¥i¯à¬O
(1) ¤£²Å¦X¨Ï¥Î±ø¥ó
(2) ¦æ¦C¦¡ªº¼ÆÈ¬° 0
µ{¦¡°õ¦æ§¹¦¨«á¡A«ö
RCL B¡BRCL C ¤À§O·|Åã¥Ü x ¤Î
y ªº¼ÆÈ¡A
¦Ó RCL D «h·|Åã¥Ü¤èµ{²Õ¦æ¦C¦¡
Determinant ªº¼ÆÈ¡C
----------------------------------------------------------------------------------------------
¤T¶¥¯x°}ªº°f¯x°}¨Ï¥Î¤èªk
¨Ò¡G pºâ¨Ò¤@¤èµ{²Õªº«Y¼Æ¯x°}
( coefficient matrix ) ªº°f¯x°} ( inverse matrix )¡C
¥ý«ö 3 EXE 4 EXE 1 EXE 1 EXE ( ¯x°}²Ä¤@¦C
( First Row )¡A²Ä¥|ӼƦr 1 ¬°¥²¶·
)
¦A«ö 1 EXE 3 EXE 1 EXE 0 EXE ( ¯x°}²Ä¤G¦C
( Second Row )¡A²Ä¥|ӼƦr 0 ¬°¥²¶·
)
¦A«ö 2 EXE -3 EXE 2 EXE 0 EXE ( ¯x°}²Ä¤T¦C
( Third Row )¡A²Ä¥|ӼƦr 0 ¬°¥²¶·
)
Åã¥Ü 0.5 ¦A«ö EXE
Åã¥Ü 0 ¦A«ö EXE
Åã¥Ü -0.5¡A¦A«ö EXE EXE
( °f¯x°}ªº²Ä¤@Äæ First Column of Inverse Matrix )
¦A«ö 3
EXE 4 EXE 1 EXE 0 EXE ( ¯x°}²Ä¤@¦C ( First Row )¡A²Ä¥|ӼƦr
0 ¬°¥²¶· )
¦A«ö 1 EXE 3 EXE 1 EXE 1 EXE ( ¯x°}²Ä¤G¦C
( Second Row )¡A²Ä¥|ӼƦr 1 ¬°¥²¶·
)
¦A«ö 2 EXE -3 EXE 2 EXE 0 EXE ( ¯x°}²Ä¤T¦C
( Third Row )¡A²Ä¥|ӼƦr 0 ¬°¥²¶·
)
Åã¥Ü -0.6111 ¦A«ö EXE
Åã¥Ü 0.2222 ¦A«ö EXE
Åã¥Ü 0.9444¡A¦A«ö EXE EXE
( °f¯x°}ªº²Ä¤GÄæ Second Column of Inverse Matrix )
¦A«ö 3
EXE 4 EXE 1 EXE 0 EXE ( ¯x°}²Ä¤@¦C ( First Row )¡A²Ä¥|ӼƦr
0 ¬°¥²¶· )
¦A«ö 1 EXE 3 EXE 1 EXE 0 EXE ( ¯x°}²Ä¤G¦C
( Second Row )¡A²Ä¥|ӼƦr 0 ¬°¥²¶·
)
¦A«ö 2 EXE -3 EXE 2 EXE 1 EXE ( ¯x°}²Ä¤T¦C
( Third Row )¡A²Ä¥|ӼƦr 1 ¬°¥²¶·
)
Åã¥Ü 0.0556 ¦A«ö EXE
Åã¥Ü -0.1111 ¦A«ö EXE
Åã¥Ü 0.2778
( °f¯x°}ªº²Ä¤TÄæ Third Column of Inverse Matrix )
¤T¶¥¯x°}ªº¦ñÀH¯x°}¨Ï¥Î¤èªk
¨Ò¡Gpºâ¨Ò¤@¤èµ{²Õªº«Y¼Æ¯x°}
( coefficient matrix ) ªº¦ñÀH¯x°} ( adjoint matrix )¡C
¥ý«eªºpºâ¤¤¤wª¾¯x°}ªº¦æ¦C¦¡ ( Determinant ) ªºÈ¬O
18¡C
¥ý«ö 3 EXE 4 EXE 1 EXE 18 EXE ( ¯x°}²Ä¤@¦C
( First Row )¡A²Ä¥|ӼƦr 18 ¬°¥²¶·
)
¦A«ö 1 EXE 3 EXE 1 EXE 0 EXE ( ¯x°}²Ä¤G¦C
( Second Row )¡A²Ä¥|ӼƦr 0 ¬°¥²¶·
)
¦A«ö 2 EXE -3 EXE 2 EXE 0 EXE ( ¯x°}²Ä¤T¦C
( Third Row )¡A²Ä¥|ӼƦr 0 ¬°¥²¶·
)
Åã¥Ü 9 ¦A«ö EXE
Åã¥Ü 0 ¦A«ö EXE
Åã¥Ü -9¡A¦A«ö EXE EXE
( ¦ñÀH¯x°}ªº²Ä¤@Äæ First Column of Adjoint Matrix )
¦A«ö 3 EXE 4 EXE 1 EXE 0 EXE ( ¯x°}²Ä¤@¦C
( First Row )¡A²Ä¥|ӼƦr 0 ¬°¥²¶·
)
¦A«ö 1 EXE 3 EXE 1 EXE 18 EXE ( ¯x°}²Ä¤G¦C
( Second Row )¡A²Ä¥|ӼƦr 18 ¬°¥²¶·
)
¦A«ö 2 EXE -3 EXE 2 EXE 0 EXE ( ¯x°}²Ä¤T¦C
( Third Row )¡A²Ä¥|ӼƦr 0 ¬°¥²¶·
)
Åã¥Ü -11 ¦A«ö EXE
Åã¥Ü 4 ¦A«ö EXE
Åã¥Ü 17¡A¦A«ö EXE EXE
( ¦ñÀH¯x°}ªº²Ä¤GÄæ Second Column of Adjoint Matrix )
¦A«ö 3 EXE 4 EXE 1 EXE 0 EXE ( ¯x°}²Ä¤@¦C
( First Row )¡A²Ä¥|ӼƦr 0 ¬°¥²¶·
)
¦A«ö 1 EXE 3 EXE 1 EXE 0 EXE ( ¯x°}²Ä¤G¦C
( Second Row )¡A²Ä¥|ӼƦr 0 ¬°¥²¶·
)
¦A«ö 2 EXE -3 EXE 2 EXE 18 EXE ( ¯x°}²Ä¤T¦C
( Third Row )¡A²Ä¥|ӼƦr 18 ¬°¥²¶·
)
Åã¥Ü 1 ¦A«ö EXE
Åã¥Ü -2 ¦A«ö EXE
Åã¥Ü 5
( ¦ñÀH¯x°}ªº²Ä¤TÄæ Third Column of Adjoint Matrix )