Mixing
Matrix vector form. Is this in the correct form?
Clash Royale CLAN TAG#URR8PPP
up vote
3
down vote
favorite
I have this question:
Write the linear system
$$beginarrayrcr-2x_1+x_2-4x_3 & = & 1 \ x_1-2x_2 & = & -3 \ x_1+x_2-4x_3 & = & 0 endarray$$
in the matrix-vector form $Amathbfx=mathbfb$.
Is this what they want?
$$
x_1*
beginbmatrix
-2 \ 1 \ 1
endbmatrix
+
x_2*
beginbmatrix
1 \ -2 \ 1
endbmatrix
+
x_3*
beginbmatrix
-4 \ 0 \ -4
endbmatrix
=
beginbmatrix
1 \ -3 \ 0
endbmatrix
$$
linear-algebra matrices systems-of-equations
edited Aug 1 at 18:42
Arnaud D.
14.5k52141
asked Aug 1 at 18:20
Jwan622
1,60111224
add a comment |Â
up vote
3
down vote
favorite
I have this question:
Write the linear system
$$beginarrayrcr-2x_1+x_2-4x_3 & = & 1 \ x_1-2x_2 & = & -3 \ x_1+x_2-4x_3 & = & 0 endarray$$
in the matrix-vector form $Amathbfx=mathbfb$.
Is this what they want?
$$
x_1*
beginbmatrix
-2 \ 1 \ 1
endbmatrix
+
x_2*
beginbmatrix
1 \ -2 \ 1
endbmatrix
+
x_3*
beginbmatrix
-4 \ 0 \ -4
endbmatrix
=
beginbmatrix
1 \ -3 \ 0
endbmatrix
$$
linear-algebra matrices systems-of-equations
edited Aug 1 at 18:42
Arnaud D.
14.5k52141
asked Aug 1 at 18:20
Jwan622
1,60111224
For general MathJax tips, you can take a look here : math.meta.stackexchange.com/questions/5020/… (See in particular the top-voted answer for matrices).
– Arnaud D.
Aug 1 at 18:48
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I have this question:
Write the linear system
$$beginarrayrcr-2x_1+x_2-4x_3 & = & 1 \ x_1-2x_2 & = & -3 \ x_1+x_2-4x_3 & = & 0 endarray$$
in the matrix-vector form $Amathbfx=mathbfb$.
Is this what they want?
$$
x_1*
beginbmatrix
-2 \ 1 \ 1
endbmatrix
+
x_2*
beginbmatrix
1 \ -2 \ 1
endbmatrix
+
x_3*
beginbmatrix
-4 \ 0 \ -4
endbmatrix
=
beginbmatrix
1 \ -3 \ 0
endbmatrix
$$
linear-algebra matrices systems-of-equations
edited Aug 1 at 18:42
Arnaud D.
14.5k52141
asked Aug 1 at 18:20
Jwan622
1,60111224
I have this question:
Write the linear system
$$beginarrayrcr-2x_1+x_2-4x_3 & = & 1 \ x_1-2x_2 & = & -3 \ x_1+x_2-4x_3 & = & 0 endarray$$
in the matrix-vector form $Amathbfx=mathbfb$.
Is this what they want?
$$
x_1*
beginbmatrix
-2 \ 1 \ 1
endbmatrix
+
x_2*
beginbmatrix
1 \ -2 \ 1
endbmatrix
+
x_3*
beginbmatrix
-4 \ 0 \ -4
endbmatrix
=
beginbmatrix
1 \ -3 \ 0
endbmatrix
$$
linear-algebra matrices systems-of-equations
edited Aug 1 at 18:42
Arnaud D.
14.5k52141
asked Aug 1 at 18:20
Jwan622
1,60111224
edited Aug 1 at 18:42
Arnaud D.
14.5k52141
edited Aug 1 at 18:42
Arnaud D.
14.5k52141
edited Aug 1 at 18:42
Arnaud D.
14.5k52141
14.5k52141
asked Aug 1 at 18:20
Jwan622
1,60111224
asked Aug 1 at 18:20
Jwan622
1,60111224
asked Aug 1 at 18:20
Jwan622
1,60111224
1,60111224
For general MathJax tips, you can take a look here : math.meta.stackexchange.com/questions/5020/… (See in particular the top-voted answer for matrices).
– Arnaud D.
Aug 1 at 18:48
add a comment |Â
For general MathJax tips, you can take a look here : math.meta.stackexchange.com/questions/5020/… (See in particular the top-voted answer for matrices).
– Arnaud D.
Aug 1 at 18:48
For general MathJax tips, you can take a look here : math.meta.stackexchange.com/questions/5020/… (See in particular the top-voted answer for matrices).
– Arnaud D.
Aug 1 at 18:48
For general MathJax tips, you can take a look here : math.meta.stackexchange.com/questions/5020/… (See in particular the top-voted answer for matrices).
– Arnaud D.
Aug 1 at 18:48
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
6
down vote
I guess the matrix-vector form here refers to the matrix A and the vector b. I would suggest to rewrite the equation in the following way
$$beginpmatrix-2&1&-4\1&-2&0\1&1&-4endpmatrixbeginpmatrixx_1\x_2\x_3endpmatrix~=~beginpmatrix1\-3\0endpmatrix$$
To verify the L.H.S. you can just multiply the vector by the matrix and then your will get first guess.
answered Aug 1 at 18:24
mrtaurho
650117
What does pmatrix mean?
– Jwan622
Aug 1 at 18:45
Why is the column of x's called a vector?
– Jwan622
Aug 1 at 18:46
The pmatrix-command gives you the $()$ braces. For other kinds of matrices just search for the LaTeX commands. How would you call a single column instead?
– mrtaurho
Aug 1 at 18:47
You can interpret this system of equation as the point of intersection within $mathbbR^3$ of the three given functions. For that every single variable represents on direction of the $3$-dimensional space you can just conclude setting the vector x as $beginpmatrixx_1\x_2\x_3endpmatrix$ where $x_1,x_2,x_3$ are the three directions towards the the $mathbbR^3$-space.
– mrtaurho
Aug 1 at 18:54
add a comment |Â
up vote
1
down vote
basically!
$
A = beginpmatrix -2 & 1 & -4 \ 1 & -2 & 0 \ 1 & 1 & -4 endpmatrix
$
and $b = beginpmatrix 1 \ -3 \ 0 endpmatrix$ yielding $Ax = b$.
answered Aug 1 at 18:22
pointguard0
641517
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
down vote
I guess the matrix-vector form here refers to the matrix A and the vector b. I would suggest to rewrite the equation in the following way
$$beginpmatrix-2&1&-4\1&-2&0\1&1&-4endpmatrixbeginpmatrixx_1\x_2\x_3endpmatrix~=~beginpmatrix1\-3\0endpmatrix$$
To verify the L.H.S. you can just multiply the vector by the matrix and then your will get first guess.
answered Aug 1 at 18:24
mrtaurho
650117
What does pmatrix mean?
– Jwan622
Aug 1 at 18:45
Why is the column of x's called a vector?
– Jwan622
Aug 1 at 18:46
The pmatrix-command gives you the $()$ braces. For other kinds of matrices just search for the LaTeX commands. How would you call a single column instead?
– mrtaurho
Aug 1 at 18:47
You can interpret this system of equation as the point of intersection within $mathbbR^3$ of the three given functions. For that every single variable represents on direction of the $3$-dimensional space you can just conclude setting the vector x as $beginpmatrixx_1\x_2\x_3endpmatrix$ where $x_1,x_2,x_3$ are the three directions towards the the $mathbbR^3$-space.
– mrtaurho
Aug 1 at 18:54
add a comment |Â
up vote
6
down vote
I guess the matrix-vector form here refers to the matrix A and the vector b. I would suggest to rewrite the equation in the following way
$$beginpmatrix-2&1&-4\1&-2&0\1&1&-4endpmatrixbeginpmatrixx_1\x_2\x_3endpmatrix~=~beginpmatrix1\-3\0endpmatrix$$
To verify the L.H.S. you can just multiply the vector by the matrix and then your will get first guess.
answered Aug 1 at 18:24
mrtaurho
650117
What does pmatrix mean?
– Jwan622
Aug 1 at 18:45
Why is the column of x's called a vector?
– Jwan622
Aug 1 at 18:46
The pmatrix-command gives you the $()$ braces. For other kinds of matrices just search for the LaTeX commands. How would you call a single column instead?
– mrtaurho
Aug 1 at 18:47
You can interpret this system of equation as the point of intersection within $mathbbR^3$ of the three given functions. For that every single variable represents on direction of the $3$-dimensional space you can just conclude setting the vector x as $beginpmatrixx_1\x_2\x_3endpmatrix$ where $x_1,x_2,x_3$ are the three directions towards the the $mathbbR^3$-space.
– mrtaurho
Aug 1 at 18:54
add a comment |Â
up vote
6
down vote
up vote
6
down vote
I guess the matrix-vector form here refers to the matrix A and the vector b. I would suggest to rewrite the equation in the following way
$$beginpmatrix-2&1&-4\1&-2&0\1&1&-4endpmatrixbeginpmatrixx_1\x_2\x_3endpmatrix~=~beginpmatrix1\-3\0endpmatrix$$
To verify the L.H.S. you can just multiply the vector by the matrix and then your will get first guess.
answered Aug 1 at 18:24
mrtaurho
650117
I guess the matrix-vector form here refers to the matrix A and the vector b. I would suggest to rewrite the equation in the following way
$$beginpmatrix-2&1&-4\1&-2&0\1&1&-4endpmatrixbeginpmatrixx_1\x_2\x_3endpmatrix~=~beginpmatrix1\-3\0endpmatrix$$
To verify the L.H.S. you can just multiply the vector by the matrix and then your will get first guess.
answered Aug 1 at 18:24
mrtaurho
650117
edited Aug 1 at 21:47
answered Aug 1 at 18:24
mrtaurho
650117
answered Aug 1 at 18:24
mrtaurho
650117
answered Aug 1 at 18:24
mrtaurho
650117
650117
What does pmatrix mean?
– Jwan622
Aug 1 at 18:45
Why is the column of x's called a vector?
– Jwan622
Aug 1 at 18:46
The pmatrix-command gives you the $()$ braces. For other kinds of matrices just search for the LaTeX commands. How would you call a single column instead?
– mrtaurho
Aug 1 at 18:47
You can interpret this system of equation as the point of intersection within $mathbbR^3$ of the three given functions. For that every single variable represents on direction of the $3$-dimensional space you can just conclude setting the vector x as $beginpmatrixx_1\x_2\x_3endpmatrix$ where $x_1,x_2,x_3$ are the three directions towards the the $mathbbR^3$-space.
– mrtaurho
Aug 1 at 18:54
add a comment |Â
What does pmatrix mean?
– Jwan622
Aug 1 at 18:45
Why is the column of x's called a vector?
– Jwan622
Aug 1 at 18:46
The pmatrix-command gives you the $()$ braces. For other kinds of matrices just search for the LaTeX commands. How would you call a single column instead?
– mrtaurho
Aug 1 at 18:47
You can interpret this system of equation as the point of intersection within $mathbbR^3$ of the three given functions. For that every single variable represents on direction of the $3$-dimensional space you can just conclude setting the vector x as $beginpmatrixx_1\x_2\x_3endpmatrix$ where $x_1,x_2,x_3$ are the three directions towards the the $mathbbR^3$-space.
– mrtaurho
Aug 1 at 18:54
What does pmatrix mean?
– Jwan622
Aug 1 at 18:45
What does pmatrix mean?
– Jwan622
Aug 1 at 18:45
Why is the column of x's called a vector?
– Jwan622
Aug 1 at 18:46
Why is the column of x's called a vector?
– Jwan622
Aug 1 at 18:46
The pmatrix-command gives you the $()$ braces. For other kinds of matrices just search for the LaTeX commands. How would you call a single column instead?
– mrtaurho
Aug 1 at 18:47
The pmatrix-command gives you the $()$ braces. For other kinds of matrices just search for the LaTeX commands. How would you call a single column instead?
– mrtaurho
Aug 1 at 18:47
You can interpret this system of equation as the point of intersection within $mathbbR^3$ of the three given functions. For that every single variable represents on direction of the $3$-dimensional space you can just conclude setting the vector x as $beginpmatrixx_1\x_2\x_3endpmatrix$ where $x_1,x_2,x_3$ are the three directions towards the the $mathbbR^3$-space.
– mrtaurho
Aug 1 at 18:54
You can interpret this system of equation as the point of intersection within $mathbbR^3$ of the three given functions. For that every single variable represents on direction of the $3$-dimensional space you can just conclude setting the vector x as $beginpmatrixx_1\x_2\x_3endpmatrix$ where $x_1,x_2,x_3$ are the three directions towards the the $mathbbR^3$-space.
– mrtaurho
Aug 1 at 18:54
add a comment |Â
up vote
1
down vote
basically!
$
A = beginpmatrix -2 & 1 & -4 \ 1 & -2 & 0 \ 1 & 1 & -4 endpmatrix
$
and $b = beginpmatrix 1 \ -3 \ 0 endpmatrix$ yielding $Ax = b$.
answered Aug 1 at 18:22
pointguard0
641517
add a comment |Â
up vote
1
down vote
basically!
$
A = beginpmatrix -2 & 1 & -4 \ 1 & -2 & 0 \ 1 & 1 & -4 endpmatrix
$
and $b = beginpmatrix 1 \ -3 \ 0 endpmatrix$ yielding $Ax = b$.
answered Aug 1 at 18:22
pointguard0
641517
add a comment |Â
up vote
1
down vote
up vote
1
down vote
basically!
$
A = beginpmatrix -2 & 1 & -4 \ 1 & -2 & 0 \ 1 & 1 & -4 endpmatrix
$
and $b = beginpmatrix 1 \ -3 \ 0 endpmatrix$ yielding $Ax = b$.
answered Aug 1 at 18:22
pointguard0
641517
basically!
$
A = beginpmatrix -2 & 1 & -4 \ 1 & -2 & 0 \ 1 & 1 & -4 endpmatrix
$
and $b = beginpmatrix 1 \ -3 \ 0 endpmatrix$ yielding $Ax = b$.
answered Aug 1 at 18:22
pointguard0
641517
answered Aug 1 at 18:22
pointguard0
641517
answered Aug 1 at 18:22
pointguard0
641517
answered Aug 1 at 18:22
pointguard0
641517
641517
add a comment |Â
add a comment |Â
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For general MathJax tips, you can take a look here : math.meta.stackexchange.com/questions/5020/… (See in particular the top-voted answer for matrices).
– Arnaud D.
Aug 1 at 18:48