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PME Journal 1:9; is there any justification for solving linear linear equation with this method?
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In the PME Journal volume 1, issue 9, archived in here, in page 359 it is given that
However, is there any justification for solving system of linear equation with this method ?
The author only provides some examples for this method in the continuation of the article, and there is not even a word why this method works.
linear-algebra systems-of-equations determinant
asked Jul 21 at 3:43
onurcanbektas
3,0611834
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up vote
2
down vote
favorite
In the PME Journal volume 1, issue 9, archived in here, in page 359 it is given that
However, is there any justification for solving system of linear equation with this method ?
The author only provides some examples for this method in the continuation of the article, and there is not even a word why this method works.
linear-algebra systems-of-equations determinant
asked Jul 21 at 3:43
onurcanbektas
3,0611834
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
In the PME Journal volume 1, issue 9, archived in here, in page 359 it is given that
However, is there any justification for solving system of linear equation with this method ?
The author only provides some examples for this method in the continuation of the article, and there is not even a word why this method works.
linear-algebra systems-of-equations determinant
asked Jul 21 at 3:43
onurcanbektas
3,0611834
In the PME Journal volume 1, issue 9, archived in here, in page 359 it is given that
However, is there any justification for solving system of linear equation with this method ?
The author only provides some examples for this method in the continuation of the article, and there is not even a word why this method works.
linear-algebra systems-of-equations determinant
asked Jul 21 at 3:43
onurcanbektas
3,0611834
edited Jul 21 at 3:50
asked Jul 21 at 3:43
onurcanbektas
3,0611834
asked Jul 21 at 3:43
onurcanbektas
3,0611834
asked Jul 21 at 3:43
onurcanbektas
3,0611834
3,0611834
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
They are (essentially) using a 'multiply and subtract' technique to simplify the equations.
E.g. Multiply 1) by $d_2$ and 2) by $d_1$. Subtract and you get 4).
You get 5) analogously with $d_3$ and $d_2$ on 2) and 3). Then, using the same idea, multiply 4) by $A_2$ and 5) by $A_1$, subtract and you get
$$|A_1B_2|y + |A_1C_2|z = 0$$
whence $fracyz = fracA_1B_2$ or $y:z = -|A_1C_2|:|A_1B_2|$.
The same thing again gives the proportion for $x$. Once you have the proportions, you can substitute and solve for the values if necessary.
answered Jul 21 at 4:08
Michael Biro
10.7k21731
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
They are (essentially) using a 'multiply and subtract' technique to simplify the equations.
E.g. Multiply 1) by $d_2$ and 2) by $d_1$. Subtract and you get 4).
You get 5) analogously with $d_3$ and $d_2$ on 2) and 3). Then, using the same idea, multiply 4) by $A_2$ and 5) by $A_1$, subtract and you get
$$|A_1B_2|y + |A_1C_2|z = 0$$
whence $fracyz = fracA_1B_2$ or $y:z = -|A_1C_2|:|A_1B_2|$.
The same thing again gives the proportion for $x$. Once you have the proportions, you can substitute and solve for the values if necessary.
answered Jul 21 at 4:08
Michael Biro
10.7k21731
add a comment |Â
up vote
3
down vote
accepted
They are (essentially) using a 'multiply and subtract' technique to simplify the equations.
E.g. Multiply 1) by $d_2$ and 2) by $d_1$. Subtract and you get 4).
You get 5) analogously with $d_3$ and $d_2$ on 2) and 3). Then, using the same idea, multiply 4) by $A_2$ and 5) by $A_1$, subtract and you get
$$|A_1B_2|y + |A_1C_2|z = 0$$
whence $fracyz = fracA_1B_2$ or $y:z = -|A_1C_2|:|A_1B_2|$.
The same thing again gives the proportion for $x$. Once you have the proportions, you can substitute and solve for the values if necessary.
answered Jul 21 at 4:08
Michael Biro
10.7k21731
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
They are (essentially) using a 'multiply and subtract' technique to simplify the equations.
E.g. Multiply 1) by $d_2$ and 2) by $d_1$. Subtract and you get 4).
You get 5) analogously with $d_3$ and $d_2$ on 2) and 3). Then, using the same idea, multiply 4) by $A_2$ and 5) by $A_1$, subtract and you get
$$|A_1B_2|y + |A_1C_2|z = 0$$
whence $fracyz = fracA_1B_2$ or $y:z = -|A_1C_2|:|A_1B_2|$.
The same thing again gives the proportion for $x$. Once you have the proportions, you can substitute and solve for the values if necessary.
answered Jul 21 at 4:08
Michael Biro
10.7k21731
They are (essentially) using a 'multiply and subtract' technique to simplify the equations.
E.g. Multiply 1) by $d_2$ and 2) by $d_1$. Subtract and you get 4).
You get 5) analogously with $d_3$ and $d_2$ on 2) and 3). Then, using the same idea, multiply 4) by $A_2$ and 5) by $A_1$, subtract and you get
$$|A_1B_2|y + |A_1C_2|z = 0$$
whence $fracyz = fracA_1B_2$ or $y:z = -|A_1C_2|:|A_1B_2|$.
The same thing again gives the proportion for $x$. Once you have the proportions, you can substitute and solve for the values if necessary.
answered Jul 21 at 4:08
Michael Biro
10.7k21731
answered Jul 21 at 4:08
Michael Biro
10.7k21731
answered Jul 21 at 4:08
Michael Biro
10.7k21731
answered Jul 21 at 4:08
Michael Biro
10.7k21731
10.7k21731
add a comment |Â
add a comment |Â
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