find an orthonormal basis for the null space of A
A = [ -1 1 -1 1 -1
2 -1 2 -1 2 ]
this is A matrix
please explain in details
thank you.
first we find basis for
nullspace A.then we apply gramschmidth orthonormalization process
on that basis to find orthonormal basis for nullspace A.
find an orthonormal basis for the null space of A A = [ -1 1 -1 1 -1 2 -1 2 -1 2 ] this is A matrix please explain in details thank you.
Find an orthonormal basis for the column space of the matrix: 2 1 3 1 -1 0
(1 point) Find a basis for the column space, row space and null space of the matrix 8 -4 4 -2 6 2 -5 -4 1 -1 -3 2 -1 Basis of column space: {T Basis of row space: OTT {{ Basis of row space: Basis of null space:
2. Compute an orthonormal basis for the null space of the linear map T: F – F given by T(a,b,c) = a + b + c.
(i) Find an orthonormal basis {~u1, ~u2} for S
(ii) Consider the function f : R3 -> R3 that to each vector ~v
assigns the vector of S given by
f(~v) = <~u1, ~v>~u1 + <~u2; ~v>~u2. Show that it is a
linear function.
(iii) What is the matrix of f in the standard basis of R3?
(iv) What are the null space and the column space of the matrix
that you computed in the
previous point?
Exercise 1. In...
Exercise 11. Given th=3(1 1 1-1)" and v2-(-1 1 3 5)T, verify that these vectors form an orthonormal set in R. Extend this set to an orthonormal basis for R4 by finding an orthonormal basis for the nullspace of 1 -1 113 5 Hint: First find a basis for the null space and then use the G-S process.
Exercise 11. Given th=3(1 1 1-1)" and v2-(-1 1 3 5)T, verify that these vectors form an orthonormal set in R. Extend...
2. Use the method of Gram-Schmidt to obtain an orthonormal basis for the column space of the matrix A- 01-2 A=121
Find a basis for the null space of each matrix given
3 3 1 B= 0 2. N(B) = {1,62,bg} 1 2. 3. b_1 b_2 |b_3 - 2 -4 -3 C= -1 3 N(C) = {ci, C2, C3, C4 } -1 -1 3 -4, |c_1 c_2 C_3 |c_4
Q1. Find a basis and dimension for row space, column space and null space for the matrix, -2 - 4 A= 3 6 -2 - 4 4 5 -6 -4 4 9 (Marks: 6)
Please answer both questions.. thank you! :)
5 4 2 1. Give A 4 5 2 (1) Numerically prove that A has an orthonormal basis of eigenvectors. (10%) (2) Find A5 by stating a proper similarity transformation (13%)
5 4 2 1. Give A 4 5 2 (1) Numerically prove that A has an orthonormal basis of eigenvectors. (10%) (2) Find A5 by stating a proper similarity transformation (13%)
solve them clear with details please thank you
Q1. Let A = be a 2 x 2 matrix. 45 (a) Find the characteristic polynomial of the matrix A. (5 pts) (b) Find all eigenvalues and associated eigenvectors of the matrix A. (10 pts) (c) If A is an eigenvalue of A, what do you think it would be the eigenvalue of the matrix 5A?Justify your answer) (5 pts) 0 Q2. Consider the matrix A = 6 2 -5 0 -6...