0 1 (5) Write the matrix A = 3 (5) Write the matrix A-B :1-pmxlindektKitary as...
5. A 3 × 3 matrix is given by A=1020 -i 0 1 (a) Verify that A is hermitian. (b) Calculate Tr (A) and det (A), where det (A) represents the determinant of A (c) Find the eigenvalues of A. Check that their product and sum are consistent with Prob. (5b) (d) Write down the diagonalized version of A (e) Find the three orthonormal eigenvectors of A. (f) Construct the unitary matrix U that diagonalizes A, and show explicitly that...
1) a) If A is a 4×5 matrix and B is a 5×2 matrix, then size of AB is: b) If C is a 3×4 matrix and size of DC is 2×4 matrix , then size of D is: c) True or False: If A and B are both 3 × 3 then AB = BA d) The 2 × 2 identity matrix is: I = e) Shade the region 3x + 2y > 6. f) Write the augmented matrix...
5. Consider the matrix A= [1 2 3 2 4 6 0 1 0 0 0 0 3 2 9 1 0 3 0] 31. 0 (a) Find a basis for C(A). (b) Find a basis for R(A). (c) Find a basis for N(A). (d) Find a basis for N(AT). (e) Write the dimension of each of these subspace.
1. Given the following matrix -4 3 0 A=-6 5 0 3 -3-1 (4 points) a. Give a diagonal matrix, D, that is similar to A. (6 points) b. Finda matrix P such that P AP D 1. Given the following matrix -4 3 0 A=-6 5 0 3 -3-1 (4 points) a. Give a diagonal matrix, D, that is similar to A. (6 points) b. Finda matrix P such that P AP D
Given the next matrixes, if possible, make the next matrix operations. A = B= foi 01 4 1 2 (0 31 1 1 2 3] 3 5 0 11 02 ſi 2 6 1 1 4 2 C = B+C (2A + 4B) (-A-B) C (A + B) AB АВС BCA
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1 0 0 2 0 0 0 0 0 0 0 0 (a) (3 pts) Let C be a matrix with rref(C) = B. Find a basis of ker(C). (b) (3 pts) Find two matrices A1 and A2 so that rref(A1) = rref(A2) im(A) # im(A2). B, and 1 (c) (5 pts) Find the matrix A with the following properties: rref(A) = B, is an...
This Question: 5 pts Perform each matrix row operation and write the new matrix. 0 1 1 1 - 1 0 1 - 6 -8 30 4 2 | 4 1 2 -5 - 3R, + R3 - 4R, + R 5 Complete the new matrix below. 00000 ODIDO 00000 00000
A) B) (1 point) The matrix A= 1-3 0 [1 0 -4 0 -1] 0 -5 has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace. The eigenvalue is -4 A basis for the eigenspace is (1 point) Find the solution to the linear system of differential equations x' y' = = 25x + 727 9 -9.2 – 26y satisfying the initial conditions x(0) = -18 and y(0) = 7. x(t) = y(t) =
5. Let A be the matrix, 0 1 2 3 0 0 1 2 A o 0 0 4 A is a nilpotent matrix. Look up the definition of a nilpotent matrix and use that along with the power series definition of the matrix exponential to find eAt 2! 5. Let A be the matrix, 0 1 2 3 0 0 1 2 A o 0 0 4 A is a nilpotent matrix. Look up the definition of a nilpotent...
1 1 5 -1 1 For the matrix A = 0 2 6 5 and the vector b = 1 0 2 0 -2 write the solution in parametric vector form. - solve the system Air b completely, and