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HW10P1 (14 points) For the following system of equations 2x1 x30 3x1 -x2 +4x3--8 4x 2...
(Has to be done by hand) HW10P1 (12 points) For the following system of equations 3x1...
(Has to be done by hand)
HW10P1 (12 points) For the following system of equations 3x1 - x2 + 4x3 = -9 -4x, + x2 + 2xy = -4 2x1 + x3 = 0 a. (2 pts) Write the linear system in the format, A x = b. b. (2 pts) Find the determinant of the matrix A by using an expansion along row 1. c. (2 pts) Find the determinant of the matrix A by using an expansion along...
need help with e f and g please 2x2 + x3 0 (1 pts) write the...
need help with e f and g please
2x2 + x3 0 (1 pts) write the linear system in the format, A x = b (2 pts) Find the determinant of the matrix A by using an expansion along row 1 (2 pts) Find the determinant of the matrix A by using an expansion along column 2 Compare the result with that of (b). Based on your result of b and/or c is matrix A singular or invertible (2 pts)...
For the following system of equations 2x1 -X2 + X3 15 2x1- x3-3 3X1 + 6X2-2x3...
For the following system of equations 2x1 -X2 + X3 15 2x1- x3-3 3X1 + 6X2-2x3 =-10 a. (2 pts) Write the linear system in the format, Ax b. b. (6 pts) Determine the adjoint matrix of the matrix A. c. (2 pts) Determine the inverse matrix using the adjoint matrix of part b. d. (2 pts) Verify your results for the inverse matrix obtained in c. e. (2 pts) Solve the system of equations using the inverse matrix verified...
Determine whether A is diagonalizable. 2 0 2 A = 0 2 2 2 2 0...
Determine whether A is diagonalizable. 2 0 2 A = 0 2 2 2 2 0 Yes No Find an invertible matrix P and a diagonal matrix D such that p-1AP = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list. If A is not diagonalizable, enter NO SOLUTION.) (D, P) = Compute the determinant using cofactor expansion along the first row and along the first column. -1 1 -1...
2. Solve the following linear systems of equations by writing the system as a matrix equation...
2. Solve the following linear systems of equations by writing the system as a matrix equation Ax = b and using the inverse of the matrix A. (You may use a calculator or computer software to find A-1. Or you can find A-1 by row-reduction.) 3x1 – 2x2 + 4x3 = 1 x1 + x2 – 2x3 = 3 2x1 + x2 + x3 = 8 321 – 2x2 + 4x3 = 10 X1 + x2 – 2x3 = 30...
1. CP1 (20 pts) Consider the system of linear equations X1 + x2 + x3 =...
1. CP1 (20 pts) Consider the system of linear equations X1 + x2 + x3 = 1 X1 - x2 + x3 = 3 - X1 + x2 + x3 = -1 a) (3 pts) Provide the Augmented matrix A for this system. b) (9 pts) Find the Row-Echelon Form (AREF) of the Augmented matrix. c) (2 pts) How many solutions does the system have? d) (6 pts) Based on the steps in part b), express Aref as a product...
HW11P1 (20 points) - LU Factorization with Partial Pivoting For the following system of equations: 4x1 -X2 + X32 2x1 (8 pts) Find the PLU factorization of the coefficients matrix, (8 pts) Solve the s...
HW11P1 (20 points) - LU Factorization with Partial Pivoting For the following system of equations: 4x1 -X2 + X32 2x1 (8 pts) Find the PLU factorization of the coefficients matrix, (8 pts) Solve the system using the PLU factorization (2 pts) Compare your PLU factorization by hand to that obtained using MATLAB. (2 pts) Compare your solution by hand to that obtained by MATLAB using the linsolve() function. a. b. c. d.
HW11P1 (20 points) - LU Factorization with Partial...
Let A be an n×n matrix. Mark each statement as true or false. Justify each answer. a. An n×n determinant is define...
Let A be an n×n matrix. Mark each statement as true or false. Justify each answer. a. An n×n determinant is defined by determinants of (n−1)×(n−1) submatrices. b. The (i,j)-cofactor of a matrix A is the matrix obtained by deleting from A its I’th row and j’th column. a. Choose the correct answer below. A. The statement is false. Although determinants of (n−1)×(n−1)submatrices can be used to find n×n determinants,they are not involved in the definition of n×n determinants. B....
1. (45 pts) Given the following system of linear equations: Xi – X2 + x3 =...
1. (45 pts) Given the following system of linear equations: Xi – X2 + x3 = X 1 + x2 + 6x3 = —2x1 + 8x2 + 4x3 = 3 (a) (3 pts) Write it in the form of Ax = b (b) (12 pts) Find all solutions of the system using Gauss elimination method. Write your answer as a column vector. (c) (4 pts) Use matrix multiplication to check your answer if possible. (d) (10 pts) Use Cramer's rule...
6. lol suppose a cubic polynomial y = a +br +cr2-dr3 goes through the points (zi, yi) for i 1, 2,...
6. lol suppose a cubic polynomial y = a +br +cr2-dr3 goes through the points (zi, yi) for i 1, 2,3,4, where r, f a, for i,j 1,2,3,4 and i f j (a) 2 Find the system of equations that determines the coefficients a, b, c and d (b) (61 Find the determinant of the coefficiant matrix using row operations, and show that the coefficient matrix is invertible. Note that you will receive no mark if you compute the determinant...
(Has to be done by hand)
HW10P1 (12 points) For the following system of equations 3x1 - x2 + 4x3 = -9 -4x, + x2 + 2xy = -4 2x1 + x3 = 0 a. (2 pts) Write the linear system in the format, A x = b. b. (2 pts) Find the determinant of the matrix A by using an expansion along row 1. c. (2 pts) Find the determinant of the matrix A by using an expansion along...
need help with e f and g please
2x2 + x3 0 (1 pts) write the linear system in the format, A x = b (2 pts) Find the determinant of the matrix A by using an expansion along row 1 (2 pts) Find the determinant of the matrix A by using an expansion along column 2 Compare the result with that of (b). Based on your result of b and/or c is matrix A singular or invertible (2 pts)...
For the following system of equations 2x1 -X2 + X3 15 2x1- x3-3 3X1 + 6X2-2x3 =-10 a. (2 pts) Write the linear system in the format, Ax b. b. (6 pts) Determine the adjoint matrix of the matrix A. c. (2 pts) Determine the inverse matrix using the adjoint matrix of part b. d. (2 pts) Verify your results for the inverse matrix obtained in c. e. (2 pts) Solve the system of equations using the inverse matrix verified...
Determine whether A is diagonalizable. 2 0 2 A = 0 2 2 2 2 0 Yes No Find an invertible matrix P and a diagonal matrix D such that p-1AP = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list. If A is not diagonalizable, enter NO SOLUTION.) (D, P) = Compute the determinant using cofactor expansion along the first row and along the first column. -1 1 -1...
2. Solve the following linear systems of equations by writing the system as a matrix equation Ax = b and using the inverse of the matrix A. (You may use a calculator or computer software to find A-1. Or you can find A-1 by row-reduction.) 3x1 – 2x2 + 4x3 = 1 x1 + x2 – 2x3 = 3 2x1 + x2 + x3 = 8 321 – 2x2 + 4x3 = 10 X1 + x2 – 2x3 = 30...
1. CP1 (20 pts) Consider the system of linear equations X1 + x2 + x3 = 1 X1 - x2 + x3 = 3 - X1 + x2 + x3 = -1 a) (3 pts) Provide the Augmented matrix A for this system. b) (9 pts) Find the Row-Echelon Form (AREF) of the Augmented matrix. c) (2 pts) How many solutions does the system have? d) (6 pts) Based on the steps in part b), express Aref as a product...
HW11P1 (20 points) - LU Factorization with Partial Pivoting For the following system of equations: 4x1 -X2 + X32 2x1 (8 pts) Find the PLU factorization of the coefficients matrix, (8 pts) Solve the system using the PLU factorization (2 pts) Compare your PLU factorization by hand to that obtained using MATLAB. (2 pts) Compare your solution by hand to that obtained by MATLAB using the linsolve() function. a. b. c. d.
HW11P1 (20 points) - LU Factorization with Partial...
1. (45 pts) Given the following system of linear equations: Xi – X2 + x3 = X 1 + x2 + 6x3 = —2x1 + 8x2 + 4x3 = 3 (a) (3 pts) Write it in the form of Ax = b (b) (12 pts) Find all solutions of the system using Gauss elimination method. Write your answer as a column vector. (c) (4 pts) Use matrix multiplication to check your answer if possible. (d) (10 pts) Use Cramer's rule...
6. lol suppose a cubic polynomial y = a +br +cr2-dr3 goes through the points (zi, yi) for i 1, 2,3,4, where r, f a, for i,j 1,2,3,4 and i f j (a) 2 Find the system of equations that determines the coefficients a, b, c and d (b) (61 Find the determinant of the coefficiant matrix using row operations, and show that the coefficient matrix is invertible. Note that you will receive no mark if you compute the determinant...
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