![2. Consider the matrix [23] A = [ 4 6+ (i) Calculate the inverse matrix exactly. (ii) Calculate the condition number on = ||A](http://img.homeworklib.com/questions/334b9180-750c-11eb-bfa5-0bb3207dedfc.png?x-oss-process=image/resize,w_560)
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2. Consider the matrix [23] A = [ 4 6+ (i) Calculate the inverse matrix exactly....
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B =...
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [
3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ]
(i) Calculate A + B,
(ii) Calculate AB
(iii) Calculate the inverse of B,
(iv) Calculate the determinant of C.
(b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2)
and (5, −1, 4) respectively.
(i) Show that P Q~ =...
Consider the following matrix: B= 5 2 - 2 3 (a) Use the Gauss-Jordan method to...
Consider the following matrix: B= 5 2 - 2 3 (a) Use the Gauss-Jordan method to obtain the matrix inverse (show all steps). (b) Calculate the condition number of the matrix. The following options correspond to only the condition number. In your written explanations, you must answer everything for parts (a) and (b). (Suggested time: 10 minutes; try to complete by 8:25 AM) None of the given answers is correct, and I will provide the correct answer in paper Condition...
U Question 6 1 pts 1 -1 1 The inverse of the matrix-1 -1 į -1...
U Question 6 1 pts 1 -1 1 The inverse of the matrix-1 -1 į -1 0 is - 10 1. Use this 1 a-b+c=2 inverse to solve the system of equations-a-b+c=-1 a+b+c= 5 ° (, -5, 2) o(-1, 2, 0) O 3 4' No 3 23 3 23
[4 points (a) Find the inverse of the matrix A= -1 2 2 3 -6 -5...
[4 points (a) Find the inverse of the matrix A= -1 2 2 3 -6 -5 2 -3 -4 using row operations. -1 + + 2.63 (b) Use your answer in part (a) to solve the system + 3.02 6.62 502 2 and state what the answer 21 2.1 9 1 means about the intersection of the 3 planes.
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue...
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
(ii) (1 pts) Use Part (i) and the method of matrix inverse to solve the following...
(ii) (1 pts) Use Part (i) and the method of matrix inverse to solve the following system of equations. Other methods receive NO credit. 1 -Y + 2 = 1 2.1 - y + 32 = 1 - +y = 2
I Consider the non-symmetric matrix (2) Show that a, = -1, 2, =23 (6) Find a...
I Consider the non-symmetric matrix (2) Show that a, = -1, 2, =23 (6) Find a generalized eigerrector is such that y1, K2, V3 - are linearly is dependent. (c) Write A in its Canonical Jordan Form.
LP PROBLEM PLEASE EXPLAIN thanks Search 3:30 Str1+2 + 23 + 4 2 + 35 (A) Calculate the optimal solution. Write the basis change in the optimal solution . (B) Find Inverse matrix B-1 of the optimal...
LP
PROBLEM PLEASE EXPLAIN
thanks
Search 3:30 Str1+2 + 23 + 4 2 + 35 (A) Calculate the optimal solution. Write the basis change in the optimal solution . (B) Find Inverse matrix B-1 of the optimal basis matrix C.) Consider increasing the constant on the right side of one constraint by 1. At that time, the smallest value of the objective function decreases most when the constant of the constraint is increased? D.) Find the range of t such...
Q5. Consider the square matrix A - 6 4 3 (a) Show that the characteristic polynomial...
Q5. Consider the square matrix A - 6 4 3 (a) Show that the characteristic polynomial of A# (X) = x-91-2. (6 pts) (b) Compute the matrix B-A 9A 21. (5 pts) (c) Show that A2 9A-21, for the given matrix A. (5 pts) (d) Is it possible to use the equation A? (Justify your answer) (5 pts) 9A 21, to incl the inverse of the given matrix A
Please answer all four questions and show work. Find the inverse of each matrix using the...
Please answer all four questions and show
work.
Find the inverse of each matrix using the reduced row echelon technique. [iii] 20. 2 1 1 [1 1 2 Show that each matrix has no inverse. [-1 2 3] 30. 5 2 0 L 2 -4 -6 For Problems 45-50, use the inverse found in Problem 19. [i 1 -17 19. 3 -1 0 1 2 -3 4 (x + y - z= 6 46.3x – y = 8 ( 2x...
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [
3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ]
(i) Calculate A + B,
(ii) Calculate AB
(iii) Calculate the inverse of B,
(iv) Calculate the determinant of C.
(b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2)
and (5, −1, 4) respectively.
(i) Show that P Q~ =...
Consider the following matrix: B= 5 2 - 2 3 (a) Use the Gauss-Jordan method to obtain the matrix inverse (show all steps). (b) Calculate the condition number of the matrix. The following options correspond to only the condition number. In your written explanations, you must answer everything for parts (a) and (b). (Suggested time: 10 minutes; try to complete by 8:25 AM) None of the given answers is correct, and I will provide the correct answer in paper Condition...
U Question 6 1 pts 1 -1 1 The inverse of the matrix-1 -1 į -1 0 is - 10 1. Use this 1 a-b+c=2 inverse to solve the system of equations-a-b+c=-1 a+b+c= 5 ° (, -5, 2) o(-1, 2, 0) O 3 4' No 3 23 3 23
[4 points (a) Find the inverse of the matrix A= -1 2 2 3 -6 -5 2 -3 -4 using row operations. -1 + + 2.63 (b) Use your answer in part (a) to solve the system + 3.02 6.62 502 2 and state what the answer 21 2.1 9 1 means about the intersection of the 3 planes.
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
(ii) (1 pts) Use Part (i) and the method of matrix inverse to solve the following system of equations. Other methods receive NO credit. 1 -Y + 2 = 1 2.1 - y + 32 = 1 - +y = 2
I Consider the non-symmetric matrix (2) Show that a, = -1, 2, =23 (6) Find a generalized eigerrector is such that y1, K2, V3 - are linearly is dependent. (c) Write A in its Canonical Jordan Form.
LP
PROBLEM PLEASE EXPLAIN
thanks
Search 3:30 Str1+2 + 23 + 4 2 + 35 (A) Calculate the optimal solution. Write the basis change in the optimal solution . (B) Find Inverse matrix B-1 of the optimal basis matrix C.) Consider increasing the constant on the right side of one constraint by 1. At that time, the smallest value of the objective function decreases most when the constant of the constraint is increased? D.) Find the range of t such...
Q5. Consider the square matrix A - 6 4 3 (a) Show that the characteristic polynomial of A# (X) = x-91-2. (6 pts) (b) Compute the matrix B-A 9A 21. (5 pts) (c) Show that A2 9A-21, for the given matrix A. (5 pts) (d) Is it possible to use the equation A? (Justify your answer) (5 pts) 9A 21, to incl the inverse of the given matrix A
Please answer all four questions and show
work.
Find the inverse of each matrix using the reduced row echelon technique. [iii] 20. 2 1 1 [1 1 2 Show that each matrix has no inverse. [-1 2 3] 30. 5 2 0 L 2 -4 -6 For Problems 45-50, use the inverse found in Problem 19. [i 1 -17 19. 3 -1 0 1 2 -3 4 (x + y - z= 6 46.3x – y = 8 ( 2x...
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