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Find a 2x2 matrix whose 2-eigenspace is the line through (2,-1) and whose kernel is the...
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2. Hint: What is the matrix of the projection onto the coordinate axis x1? Problem 5. Problem 5.4 on page 23. The following method is suggested: (1) Find an angle o such that the line x1 = –2x2 is obtained by rotating the x-axis by 0. (2) Convince yourself with geometry that to project a vector v onto the line x1 = –2x2 is the...
(1 point) Find a basis of the eigenspace associated with the eigenvalue 3 of the matrix 1 0 -4 2 3 4 1 0 5 A= 3 3 C Abasis for this eigenspace is 0 -2 0 0 1
(1 point) Find a 2 x 2 matrix A for which where E, denotes the eigenspace associated with the eigenvalue
4 2 3 13. Find a basis for the eigenspace of the matrix A1 1- corresponding to the 2 49 eigenvalue -3. [4 points.]
(1 point) Find a basis of the eigenspace associated with the eigenvalue 4 of the matrix 4044 24-2-2 10-1-5 1 01 5
Let the matrix below act on C? Find the eigenvalues and a basis for each eigenspace in c? 1 2 - 2 1 1 2 The eigenvalues of - 2 1 (Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.) are A basis for the eigenspace corresponding to the eigenvalue a + bi, where b>0, is (Type an exact answer, using radicals and i as needed.) A basis for the eigenspace...
(t point) Find a basis of the eigenspace associated wih he eigenvalue 1 of the matrix 201 2 0 10-1 -100-2 A=
Find the general solution of the system whose augmented matrix is given below. 2 -5 - 20 20 0 -15 15 0 Choose the correct answer below OA O B. O C. O D. The system has no solutions. x-2x2 5 5 x25x3 <x2=-5 X is free X is froo 3=5 x is free
Find the general solution of the system whose augmented matrix is given below. 2 -5 - 20 20 0 -15 15 0 Choose the correct answer...
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue X= 2: 4 -16 2 1 6 2 -1 8 (b) Suppose that the vector r is an eigenvector of the matrix A corresponding to the eigenvalue 1. Let n be a positive integer. What is A" equal to?
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue X= 2: 4 -1 6 2 16 2 -1 8 (b) Suppose that the vector z is an eigenvector of the matrix A corresponding to the eigenvalue 4. Let n be a positive integer. What is A"r equal to?