Reduce the following 4x4 determinant to upper triangular form and then find the determinant.
1 0 -1 3
2 2 0 0
1 0 4 -1
0 1 -5 1
Reduce the following 4x4 determinant to upper triangular form and then find the determinant. 1 0...
B: Calculate the determinant of the following matrix by using row reduction to produce an upper triangular form: 2 marks 10 4 21 B=0 -4 3 -5 -1 -12
Find the determinant by row reduction to echelon form. 1 3 1 0-4 1 0-4-2-4 0 37 5 -3
(1 point) Find the three distinct real eigenvalues of the upper-triangular matrix B= 5-7 0 0 7 -1 0 -97 -4 . 4 The eigenvalues are [Note: If there is more than one answer, separate them by commas. E.g. 1,2]
2. (10 mk) Let A 0 debe an upper triangular matrix with nonzero entries a, b, c, d, o0 f e, (a) (5 mk) Find the inverse of A. (b) (5 mk) Suppose the columns of A are eigenvectors of a matrix B. Prove that B is also upper triangular.
1 9. (5 points) Find the determinant of A= 3 3 0 0 2 0 1 -1 0 0 2 1 6 4
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...
[4 -2 0] 1. Use Gaussian reduction to find the determinant of A = |2 -1 2]. 11 5 7 [4 -2 01 2. Use the permutation expansion to find the determinant of A = 2 -1 2. 11 5 7
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...
Bonus Question for undergraduates (20 points). Mandatory for grad- uate students what is the determinant of the following matrices. Construct any example and find its determinant if it exists. (a) 2 x 3 matrix (b) Upper triangular matrix (c) 2 x 2 matrix
Problem 3 Find the determinant of the following matrix: -2 6 0 1 0 -12 10 0