Verify $U + W = {(x,x,y,z) in F^4 : x,y,z in F}$
$begingroup$
Suppose that $U = {(x,x,y,y)in F^4:x,y in mathbb F}$ and $W = {(x,x,x,y) in mathbb F^4: x,y in mathbb F}$. Then verify that
$$U + W = {(x,x,y,z) in mathbb F^4: x,y,z in mathbb F}$$
I found the solution here, but I can only follow the first few lines.
I can follow till the following lines
begin{align*} &(x_1,x_1,y_1,y_1)+(x_2,x_2,x_2,y_2)\=&(x_1+x_2,x_1+x_2,y_1+x_2,y_1+y_2) in {(x,x,y,z):x,y,zinmathbb F^4}. end{align*}
But what happens here?
linear-algebra
edited Dec 25 '18 at 4:29
zipirovich
11.4k11831
asked Dec 25 '18 at 2:06
JOHN JOHN
4589
$endgroup$
add a comment |
$begingroup$
Suppose that $U = {(x,x,y,y)in F^4:x,y in mathbb F}$ and $W = {(x,x,x,y) in mathbb F^4: x,y in mathbb F}$. Then verify that
$$U + W = {(x,x,y,z) in mathbb F^4: x,y,z in mathbb F}$$
I found the solution here, but I can only follow the first few lines.
I can follow till the following lines
begin{align*} &(x_1,x_1,y_1,y_1)+(x_2,x_2,x_2,y_2)\=&(x_1+x_2,x_1+x_2,y_1+x_2,y_1+y_2) in {(x,x,y,z):x,y,zinmathbb F^4}. end{align*}
But what happens here?
linear-algebra
edited Dec 25 '18 at 4:29
zipirovich
11.4k11831
asked Dec 25 '18 at 2:06
JOHN JOHN
4589
$endgroup$
add a comment |
$begingroup$
Suppose that $U = {(x,x,y,y)in F^4:x,y in mathbb F}$ and $W = {(x,x,x,y) in mathbb F^4: x,y in mathbb F}$. Then verify that
$$U + W = {(x,x,y,z) in mathbb F^4: x,y,z in mathbb F}$$
I found the solution here, but I can only follow the first few lines.
I can follow till the following lines
begin{align*} &(x_1,x_1,y_1,y_1)+(x_2,x_2,x_2,y_2)\=&(x_1+x_2,x_1+x_2,y_1+x_2,y_1+y_2) in {(x,x,y,z):x,y,zinmathbb F^4}. end{align*}
But what happens here?
linear-algebra
edited Dec 25 '18 at 4:29
zipirovich
11.4k11831
asked Dec 25 '18 at 2:06
JOHN JOHN
4589
$endgroup$
Suppose that $U = {(x,x,y,y)in F^4:x,y in mathbb F}$ and $W = {(x,x,x,y) in mathbb F^4: x,y in mathbb F}$. Then verify that
$$U + W = {(x,x,y,z) in mathbb F^4: x,y,z in mathbb F}$$
I found the solution here, but I can only follow the first few lines.
I can follow till the following lines
begin{align*} &(x_1,x_1,y_1,y_1)+(x_2,x_2,x_2,y_2)\=&(x_1+x_2,x_1+x_2,y_1+x_2,y_1+y_2) in {(x,x,y,z):x,y,zinmathbb F^4}. end{align*}
But what happens here?
linear-algebra
linear-algebra
edited Dec 25 '18 at 4:29
zipirovich
11.4k11831
asked Dec 25 '18 at 2:06
JOHN JOHN
4589
edited Dec 25 '18 at 4:29
zipirovich
11.4k11831
asked Dec 25 '18 at 2:06
JOHN JOHN
4589
edited Dec 25 '18 at 4:29
zipirovich
11.4k11831
edited Dec 25 '18 at 4:29
zipirovich
11.4k11831
edited Dec 25 '18 at 4:29
zipirovich
11.4k11831
11.4k11831
asked Dec 25 '18 at 2:06
JOHN JOHN
4589
asked Dec 25 '18 at 2:06
JOHN JOHN
4589
asked Dec 25 '18 at 2:06
JOHN JOHN
4589
4589
add a comment |
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
He want to prove that the two sets $U+W$ and ${(x,x,y,z)}$ are equal.
The first step is to prove $U+Wsubset{(x,x,y,z)}$ and the second is to prove ${(x,x,y,z)}subset U+W$.
To prove the second one, he construct each element of ${(x,x,y,z)}$ by using two corresponding elements in $U$ and $V$ respectively.
answered Dec 25 '18 at 2:26
W. muW. mu
760310
$endgroup$
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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active
oldest
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active
oldest
votes
$begingroup$
He want to prove that the two sets $U+W$ and ${(x,x,y,z)}$ are equal.
The first step is to prove $U+Wsubset{(x,x,y,z)}$ and the second is to prove ${(x,x,y,z)}subset U+W$.
To prove the second one, he construct each element of ${(x,x,y,z)}$ by using two corresponding elements in $U$ and $V$ respectively.
answered Dec 25 '18 at 2:26
W. muW. mu
760310
$endgroup$
add a comment |
$begingroup$
He want to prove that the two sets $U+W$ and ${(x,x,y,z)}$ are equal.
The first step is to prove $U+Wsubset{(x,x,y,z)}$ and the second is to prove ${(x,x,y,z)}subset U+W$.
To prove the second one, he construct each element of ${(x,x,y,z)}$ by using two corresponding elements in $U$ and $V$ respectively.
answered Dec 25 '18 at 2:26
W. muW. mu
760310
$endgroup$
add a comment |
$begingroup$
He want to prove that the two sets $U+W$ and ${(x,x,y,z)}$ are equal.
The first step is to prove $U+Wsubset{(x,x,y,z)}$ and the second is to prove ${(x,x,y,z)}subset U+W$.
To prove the second one, he construct each element of ${(x,x,y,z)}$ by using two corresponding elements in $U$ and $V$ respectively.
answered Dec 25 '18 at 2:26
W. muW. mu
760310
$endgroup$
He want to prove that the two sets $U+W$ and ${(x,x,y,z)}$ are equal.
The first step is to prove $U+Wsubset{(x,x,y,z)}$ and the second is to prove ${(x,x,y,z)}subset U+W$.
To prove the second one, he construct each element of ${(x,x,y,z)}$ by using two corresponding elements in $U$ and $V$ respectively.
answered Dec 25 '18 at 2:26
W. muW. mu
760310
answered Dec 25 '18 at 2:26
W. muW. mu
760310
answered Dec 25 '18 at 2:26
W. muW. mu
760310
answered Dec 25 '18 at 2:26
W. muW. mu
760310
760310
add a comment |
add a comment |
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