For each value of $t$, find an orthogonal basis of the span of the vectors:
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$u_1 = (1,t,t)$, $u_2 = (2t,t+1,2t-1)$, $u_3 = (2-2t,t-1,1)$
Any help would be appreciated, if you could explain how to work such questions out
linear-algebra vector-spaces orthogonality orthonormal change-of-basis
edited Nov 17 at 16:19
krirkrirk
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asked Nov 17 at 16:09
ankit vijay
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up vote
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down vote
favorite
$u_1 = (1,t,t)$, $u_2 = (2t,t+1,2t-1)$, $u_3 = (2-2t,t-1,1)$
Any help would be appreciated, if you could explain how to work such questions out
linear-algebra vector-spaces orthogonality orthonormal change-of-basis
edited Nov 17 at 16:19
krirkrirk
1,462518
asked Nov 17 at 16:09
ankit vijay
1
New contributor
ankit vijay is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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2
Are you familiar with the Gram-Schmidt algorithm?
– Juan Diego Rojas
Nov 17 at 16:12
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0
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up vote
0
down vote
favorite
$u_1 = (1,t,t)$, $u_2 = (2t,t+1,2t-1)$, $u_3 = (2-2t,t-1,1)$
Any help would be appreciated, if you could explain how to work such questions out
linear-algebra vector-spaces orthogonality orthonormal change-of-basis
edited Nov 17 at 16:19
krirkrirk
1,462518
asked Nov 17 at 16:09
ankit vijay
1
New contributor
ankit vijay is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$u_1 = (1,t,t)$, $u_2 = (2t,t+1,2t-1)$, $u_3 = (2-2t,t-1,1)$
Any help would be appreciated, if you could explain how to work such questions out
linear-algebra vector-spaces orthogonality orthonormal change-of-basis
linear-algebra vector-spaces orthogonality orthonormal change-of-basis
edited Nov 17 at 16:19
krirkrirk
1,462518
asked Nov 17 at 16:09
ankit vijay
1
New contributor
ankit vijay is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 17 at 16:19
krirkrirk
1,462518
asked Nov 17 at 16:09
ankit vijay
1
New contributor
ankit vijay is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 17 at 16:19
krirkrirk
1,462518
edited Nov 17 at 16:19
krirkrirk
1,462518
edited Nov 17 at 16:19
krirkrirk
1,462518
1,462518
asked Nov 17 at 16:09
ankit vijay
1
New contributor
ankit vijay is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 17 at 16:09
ankit vijay
1
asked Nov 17 at 16:09
ankit vijay
1
1
New contributor
ankit vijay is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
ankit vijay is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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2
Are you familiar with the Gram-Schmidt algorithm?
– Juan Diego Rojas
Nov 17 at 16:12
add a comment |
2
Are you familiar with the Gram-Schmidt algorithm?
– Juan Diego Rojas
Nov 17 at 16:12
2
2
Are you familiar with the Gram-Schmidt algorithm?
– Juan Diego Rojas
Nov 17 at 16:12
Are you familiar with the Gram-Schmidt algorithm?
– Juan Diego Rojas
Nov 17 at 16:12
add a comment |
1 Answer
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Step 1, check if the vectors are independent. In the general case, compute the determinant of the matrix form by the components of your vectors. In this case, just add together $u_2$ and $u_3$, then notice that it's proportional to $u_1$. So you need only two vectors in this case.
Step 2, follow the Gram-Schmidt process
answered Nov 17 at 16:28
Andrei
9,85621024
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Step 1, check if the vectors are independent. In the general case, compute the determinant of the matrix form by the components of your vectors. In this case, just add together $u_2$ and $u_3$, then notice that it's proportional to $u_1$. So you need only two vectors in this case.
Step 2, follow the Gram-Schmidt process
answered Nov 17 at 16:28
Andrei
9,85621024
add a comment |
up vote
0
down vote
Step 1, check if the vectors are independent. In the general case, compute the determinant of the matrix form by the components of your vectors. In this case, just add together $u_2$ and $u_3$, then notice that it's proportional to $u_1$. So you need only two vectors in this case.
Step 2, follow the Gram-Schmidt process
answered Nov 17 at 16:28
Andrei
9,85621024
add a comment |
up vote
0
down vote
up vote
0
down vote
Step 1, check if the vectors are independent. In the general case, compute the determinant of the matrix form by the components of your vectors. In this case, just add together $u_2$ and $u_3$, then notice that it's proportional to $u_1$. So you need only two vectors in this case.
Step 2, follow the Gram-Schmidt process
answered Nov 17 at 16:28
Andrei
9,85621024
Step 1, check if the vectors are independent. In the general case, compute the determinant of the matrix form by the components of your vectors. In this case, just add together $u_2$ and $u_3$, then notice that it's proportional to $u_1$. So you need only two vectors in this case.
Step 2, follow the Gram-Schmidt process
answered Nov 17 at 16:28
Andrei
9,85621024
answered Nov 17 at 16:28
Andrei
9,85621024
answered Nov 17 at 16:28
Andrei
9,85621024
answered Nov 17 at 16:28
Andrei
9,85621024
9,85621024
add a comment |
add a comment |
ankit vijay is a new contributor. Be nice, and check out our Code of Conduct.
ankit vijay is a new contributor. Be nice, and check out our Code of Conduct.
ankit vijay is a new contributor. Be nice, and check out our Code of Conduct.
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2
Are you familiar with the Gram-Schmidt algorithm?
– Juan Diego Rojas
Nov 17 at 16:12