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4. Solve the following system of linear equations using the inverse matrix method. 1 y = 1 2 , 3 2 -r- 1 5 4 a) x+y +z= 6 x-y-3z=-8 x+y- 2z=-6 b) Solve the following system of linear equations using Cramer's Rule. 5. 2 1 -X- 3 2 1 3 X+-y-1 5 4 y = 1 a) x+y+z= 6 x-y-3z=-8 x+y- 2z = -6 b) 4. Solve the following system of linear equations using the inverse matrix method. 1...
L. Answer True or False. Justify your answer (a) Every linear system consisting of 2 equations in 3 unknowns has infinitely many solutions (b) If A. B are n × n nonsingular matrices and AB BA, then (e) If A is an n x n matrix, with ( +A) I-A, then A O (d) If A, B two 2 x 2 symmetric matrices, then AB is also symmetric. (e) If A. B are any square matrices, then (A+ B)(A-B)-A2-B2 2....
5 1 Solve the following system of equations by using the inverse of the coefficient matrix. The inverse of the coefficient matrix is shown. 0 4 4 4 11 1 Niw w 2 2 1 А x - 2y + 3z = -1 3 13 1 -2 y - Z + W = -5 4 4 4 - 3x + 3y - 22 + 5 w = -2 3 5 1 - 1 2y - 32 + W = 3...
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...
a. Let B be an n x n Orthogonal matrix, that is B^-1 = B^T, and let A be an n x n skew-symmetric matrix. Simplify A(A^2(BA)^-1)^T b. Let A be a square matrix such that A^3 = 0. A is then called a nilpotent matrix. Define another matrix B by the expression B = I - A; Show that B is invertible and that its inverse is I + A + A^2 c. Let B = (-2,0,0 ; 0,0,0...
**C PROGRAMMING ONLY**!!!!!!! Create a script that will use Cramer's rule to find the Solutions of Ax-b for A a 3 x 3 matrix and B a 3x 1 matrix Conditions you need to use 1) User defined functions that will return value and take arguments. 2) Also, this script should use two dimensional pointer that will take care of the whole matrix Then the values of x, y and can be found as follows di bi ci ai bi...
Question 12 Consider the following system of linear equations (x-y +z = -2 x – 3y - 2 = -1 3x +2y = -8 Which of the following method can be used to solve the above system? a) Gaussian climination b) Cramer's Rule c) Inverse Matrix d) All of the mentioned Your answer 0 del Bad Ps hp
[12] QUESTION 4 (a) Let A be an m × m symmetric matrix and P be an orthogonal matrix such the PAP-D,where D is a diagonal matrix with the characteristic roots of A on the diagonal. Show that PA P is also a diagonal matrix. (b) Let A be an m × n matrix of rank m such that A = BC where B and C each has rank m. Show that (BC) CB. 16 STA4801/101/0/2019 (c) For the matrix...
4. Let A be a 4 x 4 matrix with determinant 7. Which of the following statements are correct? Justify your answer. (a) For some vector b € R4, the system of equations AT = 5 has exactly one solution. (b) For some vector 5 € R4, the system of equations Az = 5 has infinitely many solutions. (c) For some vector b E R4, the system of equations Az = has no solution. (d) For all vectors be R4,...
6.3 (Adjugate matrix) a) Let A E GLn(K). Use Cramer's rule to show that A-1 = data adj A without using Lemma 4.5.17. b) Let A Knxn be an upper triangular matrix (i.e. ajj = 0 (1 <j<i<n). Show that adj A is an upper triangular matrix. c) Let Znxn := {A € RNXN | aij € Z (i, j = 1, ..., n)}. Show that U := {A € Znxn | det(A) = 1} is a group with respect...