Mixing
Reduced row echelon form. How do get to this matrix?
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
I am reading this text and I'm stuck on how they get to the reduced row echelon form of this matrix:
I've tried a ton of combinations but I still can't get there. Can someone show me the way? Here's one that I have but then I'm stuck:
$beginmatrix
\ 1 & 2 & 5
\ 0 & -5 & -5
endmatrix$
But then how do I get rid of the 2 in the second column of the first row to 0?
linear-algebra
asked Jul 31 at 19:40
Jwan622
1,60111224
add a comment |Â
up vote
1
down vote
favorite
I am reading this text and I'm stuck on how they get to the reduced row echelon form of this matrix:
I've tried a ton of combinations but I still can't get there. Can someone show me the way? Here's one that I have but then I'm stuck:
$beginmatrix
\ 1 & 2 & 5
\ 0 & -5 & -5
endmatrix$
But then how do I get rid of the 2 in the second column of the first row to 0?
linear-algebra
asked Jul 31 at 19:40
Jwan622
1,60111224
Start by dividing two two by $-5$...
– JavaMan
Jul 31 at 19:41
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am reading this text and I'm stuck on how they get to the reduced row echelon form of this matrix:
I've tried a ton of combinations but I still can't get there. Can someone show me the way? Here's one that I have but then I'm stuck:
$beginmatrix
\ 1 & 2 & 5
\ 0 & -5 & -5
endmatrix$
But then how do I get rid of the 2 in the second column of the first row to 0?
linear-algebra
asked Jul 31 at 19:40
Jwan622
1,60111224
I am reading this text and I'm stuck on how they get to the reduced row echelon form of this matrix:
I've tried a ton of combinations but I still can't get there. Can someone show me the way? Here's one that I have but then I'm stuck:
$beginmatrix
\ 1 & 2 & 5
\ 0 & -5 & -5
endmatrix$
But then how do I get rid of the 2 in the second column of the first row to 0?
linear-algebra
asked Jul 31 at 19:40
Jwan622
1,60111224
asked Jul 31 at 19:40
Jwan622
1,60111224
asked Jul 31 at 19:40
Jwan622
1,60111224
asked Jul 31 at 19:40
Jwan622
1,60111224
1,60111224
Start by dividing two two by $-5$...
– JavaMan
Jul 31 at 19:41
add a comment |Â
Start by dividing two two by $-5$...
– JavaMan
Jul 31 at 19:41
Start by dividing two two by $-5$...
– JavaMan
Jul 31 at 19:41
Start by dividing two two by $-5$...
– JavaMan
Jul 31 at 19:41
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
1
down vote
accepted
We have
$$beginbmatrix
1 & 2 &5 \
2 & -1 & 5
endbmatrix$$
Denoting row $i$ as $r_i$ and assume that the left arrow $A leftarrow B$ means that we are putting quantity $B$ in $A$. Moreover,
we know that we can do linear operations on the rows to reach the row-echelon form, i.e.
$r_2 leftarrow r_2 - 2r_1$
$$beginbmatrix
1 & 2 &5 \
0 & -5 & -5
endbmatrix$$
$r_1 leftarrow r_1 + frac25r_2$
$$beginbmatrix
1 & 0 &3 \
0 & -5 & -5
endbmatrix$$
$r_2 leftarrow -frac15r_2$
$$beginbmatrix
1 & 0 &3 \
0 & 1 & 1
endbmatrix$$
answered Jul 31 at 19:51
Ahmad Bazzi
2,170417
add a comment |Â
up vote
1
down vote
Proceed systematically instead of trying to guess at combinations that might work. You’ve gotten a pivot in the first row and everything else in the pivot column is zero, so you move on to the second row. Find the leftmost nonzero element and divide the row by that number to make its first nonzero element a $1$. Now it should be pretty obvious what multiple of the second row to subtract from the first to zero out the element above this new pivot. If there were more to the matrix, you’d also zero out the rest of the second column, then move on to the next nonzero row. Lather, rinse, repeat.
answered Jul 31 at 19:48
amd
25.7k2943
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
We have
$$beginbmatrix
1 & 2 &5 \
2 & -1 & 5
endbmatrix$$
Denoting row $i$ as $r_i$ and assume that the left arrow $A leftarrow B$ means that we are putting quantity $B$ in $A$. Moreover,
we know that we can do linear operations on the rows to reach the row-echelon form, i.e.
$r_2 leftarrow r_2 - 2r_1$
$$beginbmatrix
1 & 2 &5 \
0 & -5 & -5
endbmatrix$$
$r_1 leftarrow r_1 + frac25r_2$
$$beginbmatrix
1 & 0 &3 \
0 & -5 & -5
endbmatrix$$
$r_2 leftarrow -frac15r_2$
$$beginbmatrix
1 & 0 &3 \
0 & 1 & 1
endbmatrix$$
answered Jul 31 at 19:51
Ahmad Bazzi
2,170417
add a comment |Â
up vote
1
down vote
accepted
We have
$$beginbmatrix
1 & 2 &5 \
2 & -1 & 5
endbmatrix$$
Denoting row $i$ as $r_i$ and assume that the left arrow $A leftarrow B$ means that we are putting quantity $B$ in $A$. Moreover,
we know that we can do linear operations on the rows to reach the row-echelon form, i.e.
$r_2 leftarrow r_2 - 2r_1$
$$beginbmatrix
1 & 2 &5 \
0 & -5 & -5
endbmatrix$$
$r_1 leftarrow r_1 + frac25r_2$
$$beginbmatrix
1 & 0 &3 \
0 & -5 & -5
endbmatrix$$
$r_2 leftarrow -frac15r_2$
$$beginbmatrix
1 & 0 &3 \
0 & 1 & 1
endbmatrix$$
answered Jul 31 at 19:51
Ahmad Bazzi
2,170417
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
We have
$$beginbmatrix
1 & 2 &5 \
2 & -1 & 5
endbmatrix$$
Denoting row $i$ as $r_i$ and assume that the left arrow $A leftarrow B$ means that we are putting quantity $B$ in $A$. Moreover,
we know that we can do linear operations on the rows to reach the row-echelon form, i.e.
$r_2 leftarrow r_2 - 2r_1$
$$beginbmatrix
1 & 2 &5 \
0 & -5 & -5
endbmatrix$$
$r_1 leftarrow r_1 + frac25r_2$
$$beginbmatrix
1 & 0 &3 \
0 & -5 & -5
endbmatrix$$
$r_2 leftarrow -frac15r_2$
$$beginbmatrix
1 & 0 &3 \
0 & 1 & 1
endbmatrix$$
answered Jul 31 at 19:51
Ahmad Bazzi
2,170417
We have
$$beginbmatrix
1 & 2 &5 \
2 & -1 & 5
endbmatrix$$
Denoting row $i$ as $r_i$ and assume that the left arrow $A leftarrow B$ means that we are putting quantity $B$ in $A$. Moreover,
we know that we can do linear operations on the rows to reach the row-echelon form, i.e.
$r_2 leftarrow r_2 - 2r_1$
$$beginbmatrix
1 & 2 &5 \
0 & -5 & -5
endbmatrix$$
$r_1 leftarrow r_1 + frac25r_2$
$$beginbmatrix
1 & 0 &3 \
0 & -5 & -5
endbmatrix$$
$r_2 leftarrow -frac15r_2$
$$beginbmatrix
1 & 0 &3 \
0 & 1 & 1
endbmatrix$$
answered Jul 31 at 19:51
Ahmad Bazzi
2,170417
answered Jul 31 at 19:51
Ahmad Bazzi
2,170417
answered Jul 31 at 19:51
Ahmad Bazzi
2,170417
answered Jul 31 at 19:51
Ahmad Bazzi
2,170417
2,170417
add a comment |Â
add a comment |Â
up vote
1
down vote
Proceed systematically instead of trying to guess at combinations that might work. You’ve gotten a pivot in the first row and everything else in the pivot column is zero, so you move on to the second row. Find the leftmost nonzero element and divide the row by that number to make its first nonzero element a $1$. Now it should be pretty obvious what multiple of the second row to subtract from the first to zero out the element above this new pivot. If there were more to the matrix, you’d also zero out the rest of the second column, then move on to the next nonzero row. Lather, rinse, repeat.
answered Jul 31 at 19:48
amd
25.7k2943
add a comment |Â
up vote
1
down vote
Proceed systematically instead of trying to guess at combinations that might work. You’ve gotten a pivot in the first row and everything else in the pivot column is zero, so you move on to the second row. Find the leftmost nonzero element and divide the row by that number to make its first nonzero element a $1$. Now it should be pretty obvious what multiple of the second row to subtract from the first to zero out the element above this new pivot. If there were more to the matrix, you’d also zero out the rest of the second column, then move on to the next nonzero row. Lather, rinse, repeat.
answered Jul 31 at 19:48
amd
25.7k2943
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Proceed systematically instead of trying to guess at combinations that might work. You’ve gotten a pivot in the first row and everything else in the pivot column is zero, so you move on to the second row. Find the leftmost nonzero element and divide the row by that number to make its first nonzero element a $1$. Now it should be pretty obvious what multiple of the second row to subtract from the first to zero out the element above this new pivot. If there were more to the matrix, you’d also zero out the rest of the second column, then move on to the next nonzero row. Lather, rinse, repeat.
answered Jul 31 at 19:48
amd
25.7k2943
Proceed systematically instead of trying to guess at combinations that might work. You’ve gotten a pivot in the first row and everything else in the pivot column is zero, so you move on to the second row. Find the leftmost nonzero element and divide the row by that number to make its first nonzero element a $1$. Now it should be pretty obvious what multiple of the second row to subtract from the first to zero out the element above this new pivot. If there were more to the matrix, you’d also zero out the rest of the second column, then move on to the next nonzero row. Lather, rinse, repeat.
answered Jul 31 at 19:48
amd
25.7k2943
answered Jul 31 at 19:48
amd
25.7k2943
answered Jul 31 at 19:48
amd
25.7k2943
answered Jul 31 at 19:48
amd
25.7k2943
25.7k2943
add a comment |Â
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2868404%2freduced-row-echelon-form-how-do-get-to-this-matrix%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Start by dividing two two by $-5$...
– JavaMan
Jul 31 at 19:41