Homework Answers
first
we form a matrix A with rows as given vectors.
then we find row reduced echelon form of A.using this we find basis for orthogonal complement of span of given vectors.
Add Answer to:
linear algebra
2. (10 points) Find a basis for the orthogonal complement of span 0 in...
0 2. (10 points) Find a basis for the orthogonal complement of span in RS
0 2. (10 points) Find a basis for the orthogonal complement of span in RS
-2 2. (10 points) Find a basis for the orthogonal complement of span -2 in R.
-2 2. (10 points) Find a basis for the orthogonal complement of span -2 in R.
linear algebra 2. (25 points) Find an orthogonal basis for the column space of the following...
linear algebra
2. (25 points) Find an orthogonal basis for the column space of the following matrix, [101] 1 0 1 1 1 1 1 0
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector v in the orthogonal co...
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector v in the orthogonal complement of the space 0 Span 2,2 Do not simply compute the cross product. (c) Let A be a 5 × 2 rnatrix with linearly independent columns. Using the rank-nullity theorem applied to AT, and any other results from the course, find the dinension of Col(A)
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector...
Advanced linear algebra thxxxxxxxx Consider the complex vector space P4(C) of polynomials of deg...
advanced linear algebra thxxxxxxxx
Consider the complex vector space P4(C) of polynomials of
degree at most 4 with coeffi- cients in C, equipped with the inner
product ⟨ , ⟩ defined by
5. Consider the complex vector space P4(C) of polynomials of degree at most 4 with coeffi- cients in C, equipped with the inner product (, ) defined by (f, g)fx)g(xJdx. (a) Find an orthogonal basis of the subspace Pi(C)span,x (b) Find the element of Pi (C) that is...
Linear Algebra -3 1. Let y=| 2 | and 1-1 I. (a) (8 pts) Find projuy...
Linear Algebra
-3 1. Let y=| 2 | and 1-1 I. (a) (8 pts) Find projuy (b) (4 pts) Find the component of y orthogonal to u. (c) (4 pts) Write y as the sum of a vector in Span u and a vector orthogonal to u (d) (4 pts) Find an orthogonal basis for R' which contains u.
How to solve all of this linear Algebra 8. (24 points total) LetV be the vector...
How to solve all of this linear
Algebra
8. (24 points total) LetV be the vector space{P2, +, *}with standard function addition and scalar multiplication Define an Inner product: <p | q>= p(0)q[O) + p(1)q(1)+ p(2)q(2). Let B = {x,x,1} a. Explain why this inner product satisfies the positive property b. Explain how you know that B forms a basis c. State the conclusions of Cauchy-Schwartz and the Triangle inequalities in terms of this inner product d. Use Gram-Schmidt and...
Linear Algebra 10. [10 points] Consider the plane P represented by the equation 2z+3y-2z = 0....
Linear Algebra
10. [10 points] Consider the plane P represented by the equation 2z+3y-2z = 0. (a) Find a basis for P. (b) Find a basis for the intersection of P with yz-plane
Find a basis for the orthognonal complement of U=span Lona i Number of Vectors: 1 Basis...
Find a basis for the orthognonal complement of U=span Lona i Number of Vectors: 1 Basis for Uł:
linear algebra (a) Use Gram-Schmidt, (using the given vectors as labeled) to find an orthonormal basis...
linear algebra
(a) Use Gram-Schmidt, (using the given vectors as labeled) to find an orthonormal basis for the span of 0 0 V3- (b) Use Gram-Schmidt, (using the given vectors as labeled) to find an orthonormal basis for the span of 0 V3-0 v2= (c) What can we conclude from the two examples computed above? Also, did you find one computation "easier than the other? If so, what do you think made it easier?
0 2. (10 points) Find a basis for the orthogonal complement of span in RS
-2 2. (10 points) Find a basis for the orthogonal complement of span -2 in R.
linear algebra
2. (25 points) Find an orthogonal basis for the column space of the following matrix, [101] 1 0 1 1 1 1 1 0
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector v in the orthogonal complement of the space 0 Span 2,2 Do not simply compute the cross product. (c) Let A be a 5 × 2 rnatrix with linearly independent columns. Using the rank-nullity theorem applied to AT, and any other results from the course, find the dinension of Col(A)
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector...
advanced linear algebra thxxxxxxxx
Consider the complex vector space P4(C) of polynomials of
degree at most 4 with coeffi- cients in C, equipped with the inner
product ⟨ , ⟩ defined by
5. Consider the complex vector space P4(C) of polynomials of degree at most 4 with coeffi- cients in C, equipped with the inner product (, ) defined by (f, g)fx)g(xJdx. (a) Find an orthogonal basis of the subspace Pi(C)span,x (b) Find the element of Pi (C) that is...
Linear Algebra
-3 1. Let y=| 2 | and 1-1 I. (a) (8 pts) Find projuy (b) (4 pts) Find the component of y orthogonal to u. (c) (4 pts) Write y as the sum of a vector in Span u and a vector orthogonal to u (d) (4 pts) Find an orthogonal basis for R' which contains u.
How to solve all of this linear
Algebra
8. (24 points total) LetV be the vector space{P2, +, *}with standard function addition and scalar multiplication Define an Inner product: <p | q>= p(0)q[O) + p(1)q(1)+ p(2)q(2). Let B = {x,x,1} a. Explain why this inner product satisfies the positive property b. Explain how you know that B forms a basis c. State the conclusions of Cauchy-Schwartz and the Triangle inequalities in terms of this inner product d. Use Gram-Schmidt and...
Linear Algebra
10. [10 points] Consider the plane P represented by the equation 2z+3y-2z = 0. (a) Find a basis for P. (b) Find a basis for the intersection of P with yz-plane
Find a basis for the orthognonal complement of U=span Lona i Number of Vectors: 1 Basis for Uł:
linear algebra
(a) Use Gram-Schmidt, (using the given vectors as labeled) to find an orthonormal basis for the span of 0 0 V3- (b) Use Gram-Schmidt, (using the given vectors as labeled) to find an orthonormal basis for the span of 0 V3-0 v2= (c) What can we conclude from the two examples computed above? Also, did you find one computation "easier than the other? If so, what do you think made it easier?
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