In this question, you will apply the Gram-Schmidt process. The subspace V has a basis of three vectors u₁= 4₂= 0 and uz (c) Normalise v₂1, to give the vector v2. Enter the answer exactly. 14 -4 1 (a) Normalise vector ₁ to give the vector v1. Note: You must enter your answer as a vector, using square brackets []. Enter each component in exact form, possibly with a square-root. For example: [1/sqrt(2), 1/sqrt(3), 1/sqrt(6)]. (b) Find the component of 2 orthogonal to ₁. Enter the answer exactly. This will become the vector v₂.
In this question, you will apply the Gram-Schmidt process. The subspace V has a basis of three vectors u₁= 4₂= 0 and uz (c) Normalise v₂1, to give the vector v2. Enter the answer exactly. 14 -4 1 (a) Normalise vector ₁ to give the vector v1. Note: You must enter your answer as a vector, using square brackets []. Enter each component in exact form, possibly with a square-root. For example: [1/sqrt(2), 1/sqrt(3), 1/sqrt(6)]. (b) Find the component of 2 orthogonal to ₁. Enter the answer exactly. This will become the vector v₂.
please help solve all of these questions much appreciated
Transcribed Image Text:In this question, you will apply the Gram-Schmidt process.
The subspace V has a basis of three vectors #₁ =
(c) Normalise v₂l, to give the vector v2. Enter the answer exactly.
(a) Normalise vector ₁ to give the vector v1.
Note: You must enter your answer as a vector, using square brackets []. Enter each component in exact form, possibly with a square-root. For example:
[1/sqrt(2), 1/sqrt(3), 1/sqrt(6)].
(f) Project the vector
(b) Find the component of 2 orthogonal to ₁. Enter the answer exactly. This will become the vector v₂!.
(g) Project the vector
42=
8
-16
6
(d) Find the component of u3 orthogonal to both v1 and v2. Enter the answer exactly. This will become the vector v3/.
5
3
(e) Normalise v3', to give the vector v3. Enter the answer exactly, possibly with a square-root. For example, the square root of 5 is entered as sqrt(5).
-3
and u3=
2
2
14
onto the same subspace.
-4
1
onto the subspace spanned by {1,2,3}.
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I am going to solve the given problem by using some simple algebra to get the required result of the given problem.
![In this question, you will apply the Gram-Schmidt process.
The subspace V has a basis of three vectors #₁ =
(c) Normalise v₂l, to give the vector v2. Enter the answer exactly.
(a) Normalise vector ₁ to give the vector v1.
Note: You must enter your answer as a vector, using square brackets []. Enter each component in exact form, possibly with a square-root. For example:
[1/sqrt(2), 1/sqrt(3), 1/sqrt(6)].
(f) Project the vector
(b) Find the component of 2 orthogonal to ₁. Enter the answer exactly. This will become the vector v₂!.
(g) Project the vector
42=
8
-16
6
(d) Find the component of u3 orthogonal to both v1 and v2. Enter the answer exactly. This will become the vector v3/.
5
3
(e) Normalise v3', to give the vector v3. Enter the answer exactly, possibly with a square-root. For example, the square root of 5 is entered as sqrt(5).
-3
and u3=
2
2
14
onto the same subspace.
-4
1
onto the subspace spanned by {1,2,3}.](https://content.bartleby.com/qna-images/question/4ac09755-9639-4075-b6f1-d2ae73f82d81/3511d82d-2661-4c03-8993-a9fea9953928/o1r8w4l_processed.png)
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