Can someone answer the two
highlighted question here
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Can someone answer the two highlighted question here Exercise 3.3.11 If A is diagonalizable, show that...
Hello, I would like to discuss with someone the work that i've done on my own...
Hello,
I would like to discuss with someone the work that i've done
on my own regarding part d).
So we have d unique eigenvalues and d < n. if d=n, then we
only have a trivial solution (by the rank nullity theorem), but
this is a contradiction because v is a non-zero eigen vector.
hence the determinant (A- \lambda*I) =0. where this determinant
is equal to the characteristic polynomial equation.
The polynomial equation p(A)= \prod (A- \lambda_i * I)...
subject: Linear Algebra if someone could answer and explain why the answers are correct that would...
subject: Linear Algebra
if someone could answer and explain why the answers
are correct that would be much appreciated. Thanks in
advance!!
Exercises 1. The set P2 of polynomials of degree less than or equal to two is a vector space under polyno- mial addition and scalar multiplication by real numbers. (a) (5 points) Show that the set A = {1, 2, 22) is a basis for P2. (b) (2 points) Find the coordinate vector of an arbitrary polynomial of...
101-2019-3-b (1).pdf-Adobe Acrobat Reader DC Eile Edit iew Window Help Home Tools 101-2019-3-b (1...
101-2019-3-b (1).pdf-Adobe Acrobat Reader DC Eile Edit iew Window Help Home Tools 101-2019-3-b (1) Sign In x Problem 2 (Eigenvalues and Eigenvectors). (a) If R2 4 R2 be defined by f(x,y) (y, x), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V -> V such that U is not an...
the last pic is number 14 please answer it as a,b,c,d as well. thanks 1. If...
the last pic is number 14 please answer it as a,b,c,d as
well.
thanks
1. If A is diagonalizable then A is diagonalizable. a) True b) The statement is incomplete c) False d) None of the above 2. In every vector space the vector (-1)u is equal to? a) -U b) All of the above c) None of the above d) u 3. The set of vectors {} is linearly dependent for a) k = 3 b) k = 1...
1- 2- 3- 1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for...
1-
2-
3-
1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
Can someone explain why the answer is A please? Exercise Suppose a test of Ho:u =...
Can someone explain why the
answer is A please?
Exercise Suppose a test of Ho:u = 7 and Ha: #7 is run with a = 0.05. The P-value of the test is 0.065. A confidence interval for u is also constructed. Of the following, which is the largest confidence level for which the confidence interval will NOT contain 7? A) 93% B) 94% C) 95% D) 96% E) 90%
Slove 4.3.8 please axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v...
Slove 4.3.8
please
axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v x (w x u) holds for all vectors w, u, and v. n= C w and (u x v) + (vxw) +(wxu) b. Show that v- a. Show that the point on the plane closest to Po has vector p given by are orthogonal Exercise 4.3.17 Show u x (vxw) = (u w)v-...
Differention Equations - Can someone answer the checked numbers please? Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve fo...
Differention Equations - Can someone answer the checked
numbers please?
Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve for A1, noting that ao- det A0 The matrix A-0 22 has characteristic equation 0 0 2 2-A)P-8-12A +62- 0, so 8A1-12+6A -A, r 8A1-12 Hence we need only divide by 8 after computing 6A+. 23 1 4 12 10 4 -64 EXERCISES 1. Find AB,...
Could someone pls explain question 9 (e)? 9. Consider the set of matrices F = a)...
Could someone pls explain question 9 (e)?
9. Consider the set of matrices F = a) Show that AB BA for all A, B E F b) Show that every A E F\ {0} is invertible and compute A-. c) Show that F is a field d) Show that F can be identified with C e) What form of matrix in F corresponds to the modđulus-argument form of a complex number Comment on the geometric significance. Solution a) Let A...
Exercise 6 (6.4.35, p.452) Let A e Cnxn, and let S be a k-dimensional subspace of...
Exercise 6 (6.4.35, p.452) Let A e Cnxn, and let S be a k-dimensional subspace of C". Then a vector ve S is called a Ritz vector of A from S if and only if there is a pie C such that the Rayleigh-Ritz-Galerkin condition Av – uv Is holds, that is, (Av – uv, s) = 0 for all s E S. The scalar u is called the Ritz value of A associated with v. Let 91, ...,qk be...
Hello,
I would like to discuss with someone the work that i've done
on my own regarding part d).
So we have d unique eigenvalues and d < n. if d=n, then we
only have a trivial solution (by the rank nullity theorem), but
this is a contradiction because v is a non-zero eigen vector.
hence the determinant (A- \lambda*I) =0. where this determinant
is equal to the characteristic polynomial equation.
The polynomial equation p(A)= \prod (A- \lambda_i * I)...
subject: Linear Algebra
if someone could answer and explain why the answers
are correct that would be much appreciated. Thanks in
advance!!
Exercises 1. The set P2 of polynomials of degree less than or equal to two is a vector space under polyno- mial addition and scalar multiplication by real numbers. (a) (5 points) Show that the set A = {1, 2, 22) is a basis for P2. (b) (2 points) Find the coordinate vector of an arbitrary polynomial of...
101-2019-3-b (1).pdf-Adobe Acrobat Reader DC Eile Edit iew Window Help Home Tools 101-2019-3-b (1) Sign In x Problem 2 (Eigenvalues and Eigenvectors). (a) If R2 4 R2 be defined by f(x,y) (y, x), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V -> V such that U is not an...
the last pic is number 14 please answer it as a,b,c,d as
well.
thanks
1. If A is diagonalizable then A is diagonalizable. a) True b) The statement is incomplete c) False d) None of the above 2. In every vector space the vector (-1)u is equal to? a) -U b) All of the above c) None of the above d) u 3. The set of vectors {} is linearly dependent for a) k = 3 b) k = 1...
1-
2-
3-
1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
Can someone explain why the
answer is A please?
Exercise Suppose a test of Ho:u = 7 and Ha: #7 is run with a = 0.05. The P-value of the test is 0.065. A confidence interval for u is also constructed. Of the following, which is the largest confidence level for which the confidence interval will NOT contain 7? A) 93% B) 94% C) 95% D) 96% E) 90%
Slove 4.3.8
please
axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v x (w x u) holds for all vectors w, u, and v. n= C w and (u x v) + (vxw) +(wxu) b. Show that v- a. Show that the point on the plane closest to Po has vector p given by are orthogonal Exercise 4.3.17 Show u x (vxw) = (u w)v-...
Differention Equations - Can someone answer the checked
numbers please?
Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve for A1, noting that ao- det A0 The matrix A-0 22 has characteristic equation 0 0 2 2-A)P-8-12A +62- 0, so 8A1-12+6A -A, r 8A1-12 Hence we need only divide by 8 after computing 6A+. 23 1 4 12 10 4 -64 EXERCISES 1. Find AB,...
Could someone pls explain question 9 (e)?
9. Consider the set of matrices F = a) Show that AB BA for all A, B E F b) Show that every A E F\ {0} is invertible and compute A-. c) Show that F is a field d) Show that F can be identified with C e) What form of matrix in F corresponds to the modđulus-argument form of a complex number Comment on the geometric significance. Solution a) Let A...
Exercise 6 (6.4.35, p.452) Let A e Cnxn, and let S be a k-dimensional subspace of C". Then a vector ve S is called a Ritz vector of A from S if and only if there is a pie C such that the Rayleigh-Ritz-Galerkin condition Av – uv Is holds, that is, (Av – uv, s) = 0 for all s E S. The scalar u is called the Ritz value of A associated with v. Let 91, ...,qk be...
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