Finding basis of $N(A)$ and $R(A)$ if elements are not real numbers
$begingroup$
The question is In the field with 4 elements F={0,1,x,y}, consider the matrix
A$=left(begin{array}{ccccc}
x & y & 0 & 0 & y \
1& 0 & x & y & y\
y & y & x & y & 0\
1 & 0 & x & y & x\
x& 0 & y & 1 & 1\
end{array}right)$
a) Compute the reduced row echelon form $A′$ of the matrix $A$.
b) Find a basis of the solution space of $A_u=0$ with $u∈F5$. (In other words, find a basis of$ N(L_A).)$
c) Find a basis of $R(L_A)$, consisting of column vectors of A.
Reminder: Some relevant formulas for the field F are $x+y=1$, $xy=1$, $x^2=y$, $y^2=x$, $1+1=0$.
I finish part a) the row echelon form and plug the formuul in to the matrix and got $A=begin{pmatrix}x&y&1&1&1\ 0&y&-y&-1&y-1\ 0&0&0&0&0\ 0&0&0&0&0\ 0&0&0&0&x-yend{pmatrix}$
how do i find the basis of N(A) and basis of R(A) if the emement is not real number
linear-algebra matrices
asked Dec 3 '18 at 22:52
Leo ChenLeo Chen
63
$endgroup$
add a comment |
$begingroup$
The question is In the field with 4 elements F={0,1,x,y}, consider the matrix
A$=left(begin{array}{ccccc}
x & y & 0 & 0 & y \
1& 0 & x & y & y\
y & y & x & y & 0\
1 & 0 & x & y & x\
x& 0 & y & 1 & 1\
end{array}right)$
a) Compute the reduced row echelon form $A′$ of the matrix $A$.
b) Find a basis of the solution space of $A_u=0$ with $u∈F5$. (In other words, find a basis of$ N(L_A).)$
c) Find a basis of $R(L_A)$, consisting of column vectors of A.
Reminder: Some relevant formulas for the field F are $x+y=1$, $xy=1$, $x^2=y$, $y^2=x$, $1+1=0$.
I finish part a) the row echelon form and plug the formuul in to the matrix and got $A=begin{pmatrix}x&y&1&1&1\ 0&y&-y&-1&y-1\ 0&0&0&0&0\ 0&0&0&0&0\ 0&0&0&0&x-yend{pmatrix}$
how do i find the basis of N(A) and basis of R(A) if the emement is not real number
linear-algebra matrices
asked Dec 3 '18 at 22:52
Leo ChenLeo Chen
63
$endgroup$
$begingroup$
1) that's not reduced row echelon form 2) you find the bases exactly as you would for matrices with real numbers.
$endgroup$
– Trevor Gunn
Dec 3 '18 at 23:54
add a comment |
$begingroup$
The question is In the field with 4 elements F={0,1,x,y}, consider the matrix
A$=left(begin{array}{ccccc}
x & y & 0 & 0 & y \
1& 0 & x & y & y\
y & y & x & y & 0\
1 & 0 & x & y & x\
x& 0 & y & 1 & 1\
end{array}right)$
a) Compute the reduced row echelon form $A′$ of the matrix $A$.
b) Find a basis of the solution space of $A_u=0$ with $u∈F5$. (In other words, find a basis of$ N(L_A).)$
c) Find a basis of $R(L_A)$, consisting of column vectors of A.
Reminder: Some relevant formulas for the field F are $x+y=1$, $xy=1$, $x^2=y$, $y^2=x$, $1+1=0$.
I finish part a) the row echelon form and plug the formuul in to the matrix and got $A=begin{pmatrix}x&y&1&1&1\ 0&y&-y&-1&y-1\ 0&0&0&0&0\ 0&0&0&0&0\ 0&0&0&0&x-yend{pmatrix}$
how do i find the basis of N(A) and basis of R(A) if the emement is not real number
linear-algebra matrices
asked Dec 3 '18 at 22:52
Leo ChenLeo Chen
63
$endgroup$
The question is In the field with 4 elements F={0,1,x,y}, consider the matrix
A$=left(begin{array}{ccccc}
x & y & 0 & 0 & y \
1& 0 & x & y & y\
y & y & x & y & 0\
1 & 0 & x & y & x\
x& 0 & y & 1 & 1\
end{array}right)$
a) Compute the reduced row echelon form $A′$ of the matrix $A$.
b) Find a basis of the solution space of $A_u=0$ with $u∈F5$. (In other words, find a basis of$ N(L_A).)$
c) Find a basis of $R(L_A)$, consisting of column vectors of A.
Reminder: Some relevant formulas for the field F are $x+y=1$, $xy=1$, $x^2=y$, $y^2=x$, $1+1=0$.
I finish part a) the row echelon form and plug the formuul in to the matrix and got $A=begin{pmatrix}x&y&1&1&1\ 0&y&-y&-1&y-1\ 0&0&0&0&0\ 0&0&0&0&0\ 0&0&0&0&x-yend{pmatrix}$
how do i find the basis of N(A) and basis of R(A) if the emement is not real number
linear-algebra matrices
linear-algebra matrices
asked Dec 3 '18 at 22:52
Leo ChenLeo Chen
63
asked Dec 3 '18 at 22:52
Leo ChenLeo Chen
63
edited Dec 3 '18 at 23:41
Leo Chen
asked Dec 3 '18 at 22:52
Leo ChenLeo Chen
63
asked Dec 3 '18 at 22:52
Leo ChenLeo Chen
63
asked Dec 3 '18 at 22:52
Leo ChenLeo Chen
63
63
$begingroup$
1) that's not reduced row echelon form 2) you find the bases exactly as you would for matrices with real numbers.
$endgroup$
– Trevor Gunn
Dec 3 '18 at 23:54
add a comment |
$begingroup$
1) that's not reduced row echelon form 2) you find the bases exactly as you would for matrices with real numbers.
$endgroup$
– Trevor Gunn
Dec 3 '18 at 23:54
$begingroup$
1) that's not reduced row echelon form 2) you find the bases exactly as you would for matrices with real numbers.
$endgroup$
– Trevor Gunn
Dec 3 '18 at 23:54
$begingroup$
1) that's not reduced row echelon form 2) you find the bases exactly as you would for matrices with real numbers.
$endgroup$
– Trevor Gunn
Dec 3 '18 at 23:54
add a comment |
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$begingroup$
1) that's not reduced row echelon form 2) you find the bases exactly as you would for matrices with real numbers.
$endgroup$
– Trevor Gunn
Dec 3 '18 at 23:54