b, where b 8. For each matrix A in Exercise 7, solve AX [10, 10, 10)....
Please solve the problem 8 only by using matrices a,b,c&d in problem 7. 7. Use elimination by pivoting to find the inverse of the following mati ces. T 2 3 2 (b) 2 24 -154 -2 ?24-27 (c)2 3 (d)1 24 5 4 6 L-213 1 1 47 (f) 3 5 2 (e) 2 1 3 5 2 5 8. For each matrix A in Exercise 7, solve Ax b, where b - [10, 10, 10].
can you help me to solve (a)? 7. Use elimination by pivoting to find the inverse of the following matri- ces. 2 -3 2. - 1 1 1 1 (b) 2 2 - 4 5 4 2 3 1 - 3 2 2 4 2 (c) 2. 3 (d) 1 -2 - 4 5 4 6. -2 -1 -3 1 4 3 (e) 2 1 3 2 - 3 -5 6 -2 5 2 5 9 4
7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operations needed to solve the system Ax b by Gauss elimination without partial pivoting. (10 marks) 7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operations needed to solve the system Ax b by Gauss elimination without...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equation of the form Ux = g , in which matrix U is an upper-triangular matrix. Show that the solution vector x may be obtained by a back-substitution algorithm, in the form Jekel (b) Iterative methods for solving Ax-b work by splitting matrix A into two...
Solve the following matrix differential equation: = Ax where A= [ 5 1 ; -2 -2] and x0 =[-3; 8]
2,3, 6, 7 1. Without matrices, solve the following system using the Gaussian elimination method + 1 + HP 6x - Sy- -2 2. Consider the following linear system of equation 3x 2 Sy- (a) Write the augmented matrix for this linear system (b) Use row operations to transform the augmented matrix into row.echelon form (label all steps) (c) Use back substitution to solve the linear system. (find x and y) x + 2y 2x = 5 3. Consider the...
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pivoting to find an upper triangular matrix U, permutation matrices Pi and P2 and lower triangular matrices Mi and M2 of the form 1 0 0 Mi-1A1 10 a2 0 1 M2 0 0 0 b1 with ail...
6. (3 -10 Consider the system = AX where A = . The matrix A has eigenvalues dt 12 -5 ) 2 = -1+2i. Find the general solution of this system. (10 pts)
Solve the equation Ax b by using the LU factorization given for A. Also solve Ax b by ordinary row reduction. 3 -5 1 0 0 3 5 4 4 A = 19 -3 1 3 -1 1 0 0 - 4 1 6 2 -6 2 3 1 0 1 58 - Let Ly b and Ux y. Solve for x and y. y X = Row reduce the augmented matrix [A b] and use it to find x...
now please (10 pts) 3. Let 0-3 8 A= -3 5 - 1 2 -5 Solve the equation (find the general solution) for Ax-2x. cos e 2-sin -cos e 2+ sin e (25 pts) 4. a) (5 pts) Find det (B) and the inverse of B, where R