Linear Equation to Matrix form
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Hey everyone I'm practicing some linear equation matrix questions, so far they're easy to construct, but I am completely lost on this one since I cannot use the method of putting them in separate columns like the normal technique used. Where do I start with this question, please anyone give me guidance?
(a) Consider the system of linear equations given by
$_1 = −x_2$
$200 x_3 = 200$
$x_3 = 4 − 3 x_4$
$100 x_2 + 100 x_3 = 100$
(i) Write the above system of equations in matrix form.
linear-algebra matrices matrix-calculus
edited Jan 23 at 11:57
amWhy
1
asked Jan 23 at 11:45
ValVal
83
$endgroup$
add a comment |
$begingroup$
Hey everyone I'm practicing some linear equation matrix questions, so far they're easy to construct, but I am completely lost on this one since I cannot use the method of putting them in separate columns like the normal technique used. Where do I start with this question, please anyone give me guidance?
(a) Consider the system of linear equations given by
$_1 = −x_2$
$200 x_3 = 200$
$x_3 = 4 − 3 x_4$
$100 x_2 + 100 x_3 = 100$
(i) Write the above system of equations in matrix form.
linear-algebra matrices matrix-calculus
edited Jan 23 at 11:57
amWhy
1
asked Jan 23 at 11:45
ValVal
83
$endgroup$
$begingroup$
So basically, the first column of your matrix corresponds to the coefficients of the $x_1$ variable. So it would look like $[1, 0, 0, 0]$ as the first column. Same for second, third, ...
$endgroup$
– TrostAft
Jan 23 at 11:48
add a comment |
$begingroup$
Hey everyone I'm practicing some linear equation matrix questions, so far they're easy to construct, but I am completely lost on this one since I cannot use the method of putting them in separate columns like the normal technique used. Where do I start with this question, please anyone give me guidance?
(a) Consider the system of linear equations given by
$_1 = −x_2$
$200 x_3 = 200$
$x_3 = 4 − 3 x_4$
$100 x_2 + 100 x_3 = 100$
(i) Write the above system of equations in matrix form.
linear-algebra matrices matrix-calculus
edited Jan 23 at 11:57
amWhy
1
asked Jan 23 at 11:45
ValVal
83
$endgroup$
Hey everyone I'm practicing some linear equation matrix questions, so far they're easy to construct, but I am completely lost on this one since I cannot use the method of putting them in separate columns like the normal technique used. Where do I start with this question, please anyone give me guidance?
(a) Consider the system of linear equations given by
$_1 = −x_2$
$200 x_3 = 200$
$x_3 = 4 − 3 x_4$
$100 x_2 + 100 x_3 = 100$
(i) Write the above system of equations in matrix form.
linear-algebra matrices matrix-calculus
linear-algebra matrices matrix-calculus
edited Jan 23 at 11:57
amWhy
1
asked Jan 23 at 11:45
ValVal
83
edited Jan 23 at 11:57
amWhy
1
asked Jan 23 at 11:45
ValVal
83
edited Jan 23 at 11:57
amWhy
1
edited Jan 23 at 11:57
amWhy
1
edited Jan 23 at 11:57
amWhy
1
1
asked Jan 23 at 11:45
ValVal
83
asked Jan 23 at 11:45
ValVal
83
asked Jan 23 at 11:45
ValVal
83
83
$begingroup$
So basically, the first column of your matrix corresponds to the coefficients of the $x_1$ variable. So it would look like $[1, 0, 0, 0]$ as the first column. Same for second, third, ...
$endgroup$
– TrostAft
Jan 23 at 11:48
add a comment |
$begingroup$
So basically, the first column of your matrix corresponds to the coefficients of the $x_1$ variable. So it would look like $[1, 0, 0, 0]$ as the first column. Same for second, third, ...
$endgroup$
– TrostAft
Jan 23 at 11:48
$begingroup$
So basically, the first column of your matrix corresponds to the coefficients of the $x_1$ variable. So it would look like $[1, 0, 0, 0]$ as the first column. Same for second, third, ...
$endgroup$
– TrostAft
Jan 23 at 11:48
$begingroup$
So basically, the first column of your matrix corresponds to the coefficients of the $x_1$ variable. So it would look like $[1, 0, 0, 0]$ as the first column. Same for second, third, ...
$endgroup$
– TrostAft
Jan 23 at 11:48
add a comment |
2 Answers
2
active
oldest
votes
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Use $1x_1 +(-1)x_2 + 0x_3 + 0x_4 = 0$ for the first row (that is $(1, -1, 0, 0)$), $0x_1 +0x_2 + 200x_3 + 0x_4 = 200$ for the second, $0x_1 +0x_2 + 1x_3 + 3x_4 = 4$ for the third, and $0x_1 +100x_2 + 100x_3 + 0x_4 = 100$ for the last.
answered Jan 23 at 11:52
lightxbulblightxbulb
945311
$endgroup$
$begingroup$
you should align your equations to make them resemble a matrix.begin{align}...end{align}
$endgroup$
– zwim
Jan 23 at 12:09
add a comment |
$begingroup$
Welcome to Math.SE. I hope you are not asking your HW question.
You can collate all the variables to one-side and constants to the other as
$begin{bmatrix} 1&1&0&0\0&0&200&0\0&0&1&3\0&100&100&0end{bmatrix}begin{bmatrix}x_1\x_2\x_3\x_4end{bmatrix}=begin{bmatrix}0\200\4\100end{bmatrix},$
thereby, forming a set of linear equation in a matrix form $Ax=b.$
answered Jan 23 at 11:50
RaajaRaaja
208312
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add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Use $1x_1 +(-1)x_2 + 0x_3 + 0x_4 = 0$ for the first row (that is $(1, -1, 0, 0)$), $0x_1 +0x_2 + 200x_3 + 0x_4 = 200$ for the second, $0x_1 +0x_2 + 1x_3 + 3x_4 = 4$ for the third, and $0x_1 +100x_2 + 100x_3 + 0x_4 = 100$ for the last.
answered Jan 23 at 11:52
lightxbulblightxbulb
945311
$endgroup$
$begingroup$
you should align your equations to make them resemble a matrix.begin{align}...end{align}
$endgroup$
– zwim
Jan 23 at 12:09
add a comment |
$begingroup$
Use $1x_1 +(-1)x_2 + 0x_3 + 0x_4 = 0$ for the first row (that is $(1, -1, 0, 0)$), $0x_1 +0x_2 + 200x_3 + 0x_4 = 200$ for the second, $0x_1 +0x_2 + 1x_3 + 3x_4 = 4$ for the third, and $0x_1 +100x_2 + 100x_3 + 0x_4 = 100$ for the last.
answered Jan 23 at 11:52
lightxbulblightxbulb
945311
$endgroup$
$begingroup$
you should align your equations to make them resemble a matrix.begin{align}...end{align}
$endgroup$
– zwim
Jan 23 at 12:09
add a comment |
$begingroup$
Use $1x_1 +(-1)x_2 + 0x_3 + 0x_4 = 0$ for the first row (that is $(1, -1, 0, 0)$), $0x_1 +0x_2 + 200x_3 + 0x_4 = 200$ for the second, $0x_1 +0x_2 + 1x_3 + 3x_4 = 4$ for the third, and $0x_1 +100x_2 + 100x_3 + 0x_4 = 100$ for the last.
answered Jan 23 at 11:52
lightxbulblightxbulb
945311
$endgroup$
Use $1x_1 +(-1)x_2 + 0x_3 + 0x_4 = 0$ for the first row (that is $(1, -1, 0, 0)$), $0x_1 +0x_2 + 200x_3 + 0x_4 = 200$ for the second, $0x_1 +0x_2 + 1x_3 + 3x_4 = 4$ for the third, and $0x_1 +100x_2 + 100x_3 + 0x_4 = 100$ for the last.
answered Jan 23 at 11:52
lightxbulblightxbulb
945311
edited Jan 23 at 12:37
answered Jan 23 at 11:52
lightxbulblightxbulb
945311
answered Jan 23 at 11:52
lightxbulblightxbulb
945311
answered Jan 23 at 11:52
lightxbulblightxbulb
945311
945311
$begingroup$
you should align your equations to make them resemble a matrix.begin{align}...end{align}
$endgroup$
– zwim
Jan 23 at 12:09
add a comment |
$begingroup$
you should align your equations to make them resemble a matrix.begin{align}...end{align}
$endgroup$
– zwim
Jan 23 at 12:09
$begingroup$
you should align your equations to make them resemble a matrix.
begin{align}...end{align}$endgroup$
– zwim
Jan 23 at 12:09
$begingroup$
you should align your equations to make them resemble a matrix.
begin{align}...end{align}$endgroup$
– zwim
Jan 23 at 12:09
add a comment |
$begingroup$
Welcome to Math.SE. I hope you are not asking your HW question.
You can collate all the variables to one-side and constants to the other as
$begin{bmatrix} 1&1&0&0\0&0&200&0\0&0&1&3\0&100&100&0end{bmatrix}begin{bmatrix}x_1\x_2\x_3\x_4end{bmatrix}=begin{bmatrix}0\200\4\100end{bmatrix},$
thereby, forming a set of linear equation in a matrix form $Ax=b.$
answered Jan 23 at 11:50
RaajaRaaja
208312
$endgroup$
add a comment |
$begingroup$
Welcome to Math.SE. I hope you are not asking your HW question.
You can collate all the variables to one-side and constants to the other as
$begin{bmatrix} 1&1&0&0\0&0&200&0\0&0&1&3\0&100&100&0end{bmatrix}begin{bmatrix}x_1\x_2\x_3\x_4end{bmatrix}=begin{bmatrix}0\200\4\100end{bmatrix},$
thereby, forming a set of linear equation in a matrix form $Ax=b.$
answered Jan 23 at 11:50
RaajaRaaja
208312
$endgroup$
add a comment |
$begingroup$
Welcome to Math.SE. I hope you are not asking your HW question.
You can collate all the variables to one-side and constants to the other as
$begin{bmatrix} 1&1&0&0\0&0&200&0\0&0&1&3\0&100&100&0end{bmatrix}begin{bmatrix}x_1\x_2\x_3\x_4end{bmatrix}=begin{bmatrix}0\200\4\100end{bmatrix},$
thereby, forming a set of linear equation in a matrix form $Ax=b.$
answered Jan 23 at 11:50
RaajaRaaja
208312
$endgroup$
Welcome to Math.SE. I hope you are not asking your HW question.
You can collate all the variables to one-side and constants to the other as
$begin{bmatrix} 1&1&0&0\0&0&200&0\0&0&1&3\0&100&100&0end{bmatrix}begin{bmatrix}x_1\x_2\x_3\x_4end{bmatrix}=begin{bmatrix}0\200\4\100end{bmatrix},$
thereby, forming a set of linear equation in a matrix form $Ax=b.$
answered Jan 23 at 11:50
RaajaRaaja
208312
answered Jan 23 at 11:50
RaajaRaaja
208312
answered Jan 23 at 11:50
RaajaRaaja
208312
answered Jan 23 at 11:50
RaajaRaaja
208312
208312
add a comment |
add a comment |
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$begingroup$
So basically, the first column of your matrix corresponds to the coefficients of the $x_1$ variable. So it would look like $[1, 0, 0, 0]$ as the first column. Same for second, third, ...
$endgroup$
– TrostAft
Jan 23 at 11:48