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
1
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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
1,458518
asked Nov 17 at 16:09
ankit vijay
1
2
Are you familiar with the Gram-Schmidt algorithm?
– Juan Diego Rojas
Nov 17 at 16:12
add a comment |
up vote
0
down vote
favorite
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
1,458518
asked Nov 17 at 16:09
ankit vijay
1
$u_1 = (1,t,t)$, $u_2 = (2t,t+1,2t-1)$, $u_3 = (2-2t,t-1,1)$
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
1,458518
asked Nov 17 at 16:09
ankit vijay
1
edited Nov 17 at 16:19
krirkrirk
1,458518
asked Nov 17 at 16:09
ankit vijay
1
edited Nov 17 at 16:19
krirkrirk
1,458518
edited Nov 17 at 16:19
krirkrirk
1,458518
edited Nov 17 at 16:19
krirkrirk
1,458518
1,458518
asked Nov 17 at 16:09
ankit vijay
1
asked Nov 17 at 16:09
ankit vijay
1
asked Nov 17 at 16:09
ankit vijay
1
1
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
10.3k21025
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
10.3k21025
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
10.3k21025
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
10.3k21025
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
10.3k21025
answered Nov 17 at 16:28
Andrei
10.3k21025
answered Nov 17 at 16:28
Andrei
10.3k21025
answered Nov 17 at 16:28
Andrei
10.3k21025
10.3k21025
add a comment |
add a comment |
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Are you familiar with the Gram-Schmidt algorithm?
– Juan Diego Rojas
Nov 17 at 16:12