A1 | B1 | C1 | D1 | E1 |
Matrix1&determinant | ||||
A11*X+A12*Y=C1 | ||||
A21*X+A22*Y=C2 | ||||
EXAMPLE1 | ||||
X+Y=5 | EQ_1 | |||
X-Y=1 | EQ_2 | |||
1 | 1 | = | 5 | |
1 | -1 | 1 | ||
X=DX/D | ||||
Y=DY/D | ||||
DX= | C1 | A12 | ||
C2 | A22 | =(C1*A22-C2*A12) | ||
-6.00 | ||||
DY= | A11 | C1 | ||
A21 | C2 | =(A11*C2-C1*A21) | ||
-4.00 | ||||
D=DELTA | A11 | A12 | ||
A21 | A22 | =(A11*A22-A12*A21) | ||
-2.00 | ||||
X=DX/D | 3 | ANS1 | ||
Y=DY/D | 2 | ANS2 | ||
application in electric circuit | ||||
A16 | B16 | C16 | ||
E1-E2=I1*r1+(I1+I2)r2 | EQ_1 | sumE=sum(Ii*ri) | ||
E3-E2=I2*r3+(I1+I2)r2 | EQ_2 | sumE=sum(Ii*ri) | ||
E1-E2=(r1+r2)*I1+r2*I2 | EQ_1 | A11*I1+A12*I2=C1 | ||
E3-E2=r2*I1+(r2+r3)*I2 | EQ_2 | A21*I1+A22*I2=C2 | ||
Electric_Cell_no. | E i(V) | r i(ohm) | ||
1 | 3 | 3 | ||
2 | 1 | 1 | ||
3 | 2 | 2 | ||
A11=r1+r2 | 4 | |||
A12=r2 | 1 | |||
A21=r2 | 1 | |||
A22=r2+r3 | 3 | |||
C1=E1-E2 | 2 | |||
C2=E3-E2 | 1 | |||
DI1= | C1 | A12 | ||
C2 | A22 | |||
= | 2 | 1 | 5 | |
1 | 3 | |||
DI2= | A11 | C1 | ||
A21 | C2 | |||
= | 4 | 2 | 2 | |
1 | 1 | |||
D= | A11 | A12 | ||
A21 | A22 | |||
= | 4 | 1 | 11 | |
1 | 3 | |||
I1=DI1/D | 0.455 | ANS1 | ||
I2=DI2/D | 0.182 | ANS2 | ||
I1+I2= | 0.636 | ANS3 | ||
External_P.D._E1=E1-I1*r1 | 1.636 | discharge_I | ||
External_P.D._E2=E2+(I1+I2)*r2 | 1.636 | charge_I | ||
External_P.D._E3=E3-I2*r3 | 1.636 | discharge_I | ||
application in electric circuit | |||
A16 | B16 | C16 | |
E1-E2=I1*r1+(I1+I2)r2 | EQ_1 | sumE=sum(Ii*ri) | |
E3-E2=I2*r3+(I1+I2)r2 | EQ_2 | sumE=sum(Ii*ri) | |
E1-E2=(r1+r2)*I1+r2*I2 | EQ_1 | A11*I1+A12*I2=C1 | |
E3-E2=r2*I1+(r2+r3)*I2 | EQ_2 | A21*I1+A22*I2=C2 | |
Electric_Cell_no. | E i(V) | r i(ohm) | |
1 | 1.5 | 5 | |
2 | 1.5 | 5 | |
3 | 1.5 | 5 | |
A11=r1+r2 | 10 | ||
A12=r2 | 5 | ||
A21=r2 | 5 | ||
A22=r1+r2 | 10 | ||
C1=E1-E2 | 0 | ||
C2=E3-E2 | 0 | ||
DI1= | C1 | A12 | |
C2 | A22 | ||
= | 0 | 5 | 0 |
0 | 10 | ||
DI2= | A11 | C1 | |
A21 | C2 | ||
= | 10 | 0 | 0 |
5 | 0 | ||
D= | A11 | A12 | |
A21 | A22 | ||
= | 10 | 5 | 75 |
5 | 10 | ||
I1=DI1/D | 0.000 | ANS1 | |
I2=DI2/D | 0.000 | ANS2 | |
I1+I2= | 0.000 | ANS3 | |
External_P.D._E1=E1-I1*r1 | 1.500 | discharge_I | |
External_P.D._E2=E2+(I1+I2)*r2 | 1.500 | charge_I | |
External_P.D._E3=E3-I2*r3 | 1.500 | discharge_I |
application in electric circuit | |||
A16 | B16 | C16 | |
E1-E2=I1*r1+(I1+I2)r2 | EQ_1 | sumE=sum(Ii*ri) | |
E3-E2=I2*r3+(I1+I2)r2 | EQ_2 | sumE=sum(Ii*ri) | |
E1-E2=(r1+r2)*I1+r2*I2 | EQ_1 | A11*I1+A12*I2=C1 | |
E3-E2=r2*I1+(r2+r3)*I2 | EQ_2 | A21*I1+A22*I2=C2 | |
Electric_Cell_no. | E i(V) | r i(ohm) | |
1 | 15 | 10 | |
2 | 0 | 10 | |
3 | 0 | 10 | |
A11=r1+r2 | 20 | ||
A12=r2 | 10 | ||
A21=r2 | 10 | ||
A22=r1+r2 | 20 | ||
C1=E1-E2 | 15 | ||
C2=E3-E2 | 0 | ||
DI1= | C1 | A12 | |
C2 | A22 | ||
= | 15 | 10 | 300 |
0 | 20 | ||
DI2= | A11 | C1 | |
A21 | C2 | ||
= | 20 | 15 | -150 |
10 | 0 | ||
D= | A11 | A12 | |
A21 | A22 | ||
= | 20 | 10 | 300 |
10 | 20 | ||
I1=DI1/D | 1.000 | ANS1 | |
I2=DI2/D | -0.500 | ANS2 | |
I1+I2= | 0.500 | ANS3 | |
External_P.D._E1=E1-I1*r1 | 5.000 | discharge_I | |
External_P.D._E2=E2+(I1+I2)*r2 | 5.000 | charge_I | |
External_P.D._E3=E3-I2*r3 | 5.000 | discharge_I |
edit @ 2006/08/17 00:14:06
edit @ 2006/08/17 00:20:57
edit @ 2006/08/17 00:35:15
