3. Consider the matrix A with an unspecified entry k: 10-11 A = 1 1 11...
Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08 a Find the cofactors C11,C2,C3 of A. b Find the determinant of 1, det(A) [ 2 4 61 Problem 2 Consider the matriz A=008 | 2 5 3 a Use the ero's to put A in upper triangular form 5 Pinul the determinant of A. (A) by keeping track of the row operations in part a and the properties of determinant Problem 3 Consider...
Question 1 of 8 1.0 Points 11 [100] [o 1 1] , B= 0 1 2 and C = 0 1 2. Which of 10 3 4 10 3 4] Consider the matrices A= 3 4 these matrices is/are invertible? O A. All of them O B. A and B only O C. A and C only OD. B and C only O E. None of them Reset Selection Part 2 of 7 - Question 2 of 8 1.0 Points...
Explain all parts of question 1 and question 2 in detail
1. Consider the matrix In + Inn, which has every diagonal entry equal to 2 and every off-diagonal entry equal to 1. (a) Compute det(In + Inn) for each of n = 1,2,3. (b) For n = 4, we have 2 1 1 1 1 2 1 1 1 1 2 1 111 2 2 1 1 1 -1 1 0 0 -1 0 1 0 -1 0 0...
(2) (15 marks) Consider matrices 2 A= and B= 8 12 -2 3 b= = [] (VI) (2 marks) Find A16 by writing 7 as linear combination of eigenvectors of A. (VII) (2 marks) Find a formula for Ak for all non-negative integers k. (Can k be a negative integer?) (VIII) (1 mark) Use (VII) to find Alº7 and compare it with what you found in (VI). (IX) (2 mark) Is A similar to B? If yes, find an invertible...
Given the matrix 5 28 -16 A = 1 8 -4 E R3x3, 3 21 -11 1. find all eigenvalues of A, 2. find the corresponding eigenvectors of A 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that K-IAK = D.
Find all the values of k for which the following matrix is invertible [k-1 k-1 0 k2 2 k 0 k-1 k-1
For the following problems use: Annx n matrix A is invertible RREF(A) = I rank(A) - n A 2 x 2 matrix A is invertible = det(A) 0 3 singular (non-invertible). For which value(s) of h is A = -2 -1 -4 Choose... Choose... 6 2 h-2 a 0,b 0,c+0,d +0 A = 4 -1 C 0 x-2 or x 4 For which values of x is A = invertible a 0,b 0,c 0,d=0 4 x 2 X#1 and x2...
14. (1 mark) Let 4-1 = 1-1 -3 11 17 -2 , find the value of a. I c d A: 2 B: 3 C: 1 |D: -- | E: 11 15. (1 mark) Find the value(s) of k for which the matrix A= 1 -1 0 1 1 0 -1 has an inverse. -6 2 k E: all values of k| A: no value of k B: all k = 4 C: k = 0 D: k= 4
(1 2 0 1 11. Consider the matrix A = (3 0 1 ) 10 2 -1) (a) Are the columns of A are linearly independent? Justify your answer. Is A invertible? (b) Compute factors L and U so that A = LU, with L unit lower triangular and U upper triangular. Please show your work.
Verify the following properties, using any distinct, invertible
A, B, 4×4 upper triangular matrices of your choice:
3. (0.5 marks each) Verify the following properties, using any distinct, invertible A, B, 4 x 4 upper triangular matrices of your choice: (a) The inverse of an upper triangular matrix is upper triangular; (b) (AB)- B-1A-1 (e) trace(AB) trace(BA); (d) det(AB) det (BA) example of matrices A, B such that det(AB) det(BA) (BONUS 1 mark) Give an
3. (0.5 marks each) Verify...