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PROBLEM 3 (20%) Evaluate the following determinants: PROBLEM-i120%) Given the matrix 3 3 1 (a Fin...
1 EXERCISE 5.2 1. Evaluate the following determinants:
EXERCISE 5.2 1. Evaluate the following determinants: 2. Determine the signs to be attached to the relevant minors in order to get the following cofactors of a determinant: (C13l, IC23i, (C3sl. Canl, and Cu). 6. Find the minors and cofactors of the third row, given EXERCISE 5.3 4. Test whether the following matrices are nonsingular: EXERCISE 5.4 4. Find the inverse of each of the following matrices: 6. Solve the system Ax=d by matrix inversion, where EXERCISE 5.5 1. Use Cramer's rule to solve the following equation systems: 3. Use Cramer's...
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforwar...
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforward Gauss (or Jordan) elimination (Problem 7 is a particular case for n 3). First you write down the augmented matrix A and apply the Gauss process to this as discussed in class: A-la2,1 a2,2 a2,n : an,1 an,2 .. an.n 0 0 1 3. Derive the Jordan elimination algorithm without pivoting for the augmented matrix in terms of a triple...
5. For the system, 4x + y + 2z = 1 2x + 3y + 4z...
5. For the system, 4x + y + 2z = 1 2x + 3y + 4z = -5 x – y +3z = 3 Find the rank of the coefficient matrix by calculating the determinant. Use Cramer's theorem to find the solution of this system. (10 points) 6. Find the inverse of the following matrix using Gauss-Jordan method. Verify your result by computing the inverse using the method of determinants. (10 points) 1 2 4 2 4 2 1] 1...
Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73,...
Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73, 74, and has determinant det A = 1. Find the following determinants: ☺ U2 ü det 604 det det A +50 Note: You can earn partial creat on this problem Problem 1. (50 points) Let Rem -5 -20 -1 -1 - 1 4 16 0 الها (a) Compute dexA Use Cramer's rule to solve the following system 20x -5x -X -4 3 + 16x9...
Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08...
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...
1. Algebra: Why are all these determinants zero? 3 -1 6 21 1 0 0 0...
1. Algebra: Why are all these determinants zero? 3 -1 6 21 1 0 0 0 1 -2 3 -4 1 3 1 2 7 -1 2 2 1 3 5 2 3 4 5 (a) 1 1 1 1 1; (b) 2 5 2; (c) 3 0 1 -73 (d) 3 1 7 11 3 7 3 3 -1 6 21 5 2 6 10 3 3 3 3 2. Algebra: - la b c Given that d e...
(1 point) Consider the following Gauss elimination: i [-9 | | |- |- |- |- |-...
(1 point) Consider the following Gauss elimination: i [-9 | | |- |- |- |- |- |- | ſi 081 0 1 0 1 Lo 0 1] 100 0 0 1 EA A+ 0 EE, A O 0 0 1 -8 0 E, EEA 0 1 4 17 -7 7 0 3 0 1 0 0 0 What is the determinant of A? det(A) = (1 point) Given the matrix find all values of a that make A = 0....
(6 points) Evaluate the following system using the augmented matrix method. When performing row reduction, be...
(6 points) Evaluate the following system using the augmented matrix method. When performing row reduction, be sure to indicate your row operations. x 2x -x + 2y + 5y + 4y – + – 2= z = 2z = -3 1 3 (12 points) Evaluate the following system using Gauss-Jordan elimination. When per- forming row reduction, be sure to indicate your row operations. 2x x -x (a) – + + y + z = y + 2z = 3y +...
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A us...
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...
Total(25 marks) 3. Given the system of equation as 3x + 7y - 2z=2 x -...
Total(25 marks) 3. Given the system of equation as 3x + 7y - 2z=2 x - 5y + z = 13 2x + 3y - 102=-23 (a) Write a Matlab/C++ computer program to solve the system of linear equations based of the partial/scaled pivoting technique in Q3b below/ You can use any programming language] CR(10) An(9) AP(3) An(3) (b)Solve the system of equation using Gauss-Jordan Elimination method Hence Find the ii) Determinant of the matrix A, the coefficient Matrix of...
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforward Gauss (or Jordan) elimination (Problem 7 is a particular case for n 3). First you write down the augmented matrix A and apply the Gauss process to this as discussed in class: A-la2,1 a2,2 a2,n : an,1 an,2 .. an.n 0 0 1 3. Derive the Jordan elimination algorithm without pivoting for the augmented matrix in terms of a triple...
5. For the system, 4x + y + 2z = 1 2x + 3y + 4z = -5 x – y +3z = 3 Find the rank of the coefficient matrix by calculating the determinant. Use Cramer's theorem to find the solution of this system. (10 points) 6. Find the inverse of the following matrix using Gauss-Jordan method. Verify your result by computing the inverse using the method of determinants. (10 points) 1 2 4 2 4 2 1] 1...
Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73, 74, and has determinant det A = 1. Find the following determinants: ☺ U2 ü det 604 det det A +50 Note: You can earn partial creat on this problem Problem 1. (50 points) Let Rem -5 -20 -1 -1 - 1 4 16 0 الها (a) Compute dexA Use Cramer's rule to solve the following system 20x -5x -X -4 3 + 16x9...
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...
1. Algebra: Why are all these determinants zero? 3 -1 6 21 1 0 0 0 1 -2 3 -4 1 3 1 2 7 -1 2 2 1 3 5 2 3 4 5 (a) 1 1 1 1 1; (b) 2 5 2; (c) 3 0 1 -73 (d) 3 1 7 11 3 7 3 3 -1 6 21 5 2 6 10 3 3 3 3 2. Algebra: - la b c Given that d e...
(1 point) Consider the following Gauss elimination: i [-9 | | |- |- |- |- |- |- | ſi 081 0 1 0 1 Lo 0 1] 100 0 0 1 EA A+ 0 EE, A O 0 0 1 -8 0 E, EEA 0 1 4 17 -7 7 0 3 0 1 0 0 0 What is the determinant of A? det(A) = (1 point) Given the matrix find all values of a that make A = 0....
(6 points) Evaluate the following system using the augmented matrix method. When performing row reduction, be sure to indicate your row operations. x 2x -x + 2y + 5y + 4y – + – 2= z = 2z = -3 1 3 (12 points) Evaluate the following system using Gauss-Jordan elimination. When per- forming row reduction, be sure to indicate your row operations. 2x x -x (a) – + + y + z = y + 2z = 3y +...
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...
Total(25 marks) 3. Given the system of equation as 3x + 7y - 2z=2 x - 5y + z = 13 2x + 3y - 102=-23 (a) Write a Matlab/C++ computer program to solve the system of linear equations based of the partial/scaled pivoting technique in Q3b below/ You can use any programming language] CR(10) An(9) AP(3) An(3) (b)Solve the system of equation using Gauss-Jordan Elimination method Hence Find the ii) Determinant of the matrix A, the coefficient Matrix of...
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