(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and...
3. Find the inverse of the following matrix: (5 pts) B=11 2-3 hy row rednicing the 3x 6 matrices pl 3, where 13 denotes the 3 3 identity nu trix
1 3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1 3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1
1. Find the row echelon form for each of the following matrices: 2 -3 -27 (a) 2 1 1 [ 221] 1 - 2 -4 1] 1 3 7 2 2 1 -12 -11 -16 5 To 1 37 1-30 2 -6 2 Lo 14
Find the inverse in row operations [2111111−11] Find the inverse: [1212−1211−2] Find the inverse: [6233111034] Find the solution to Ax= b where A = [2111111−11]and b = [2−53] For each of the three matrices above, find L and U such that A=LU Find the solution to Ax=b where: A = [1212−1211−2]and b = 211 2 2 1 2 1 121 314 630 211 We were unable to transcribe this imageWe were unable to transcribe this image14-5
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [ 3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ] (i) Calculate A + B, (ii) Calculate AB (iii) Calculate the inverse of B, (iv) Calculate the determinant of C. (b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2) and (5, −1, 4) respectively. (i) Show that P Q~ =...
3) Find K such that the following matrices are singular 1 2 -11 11 1 -2] (ii) -34 K (iii) 3 -1 11 4 3 4 26k 3 -6 IK 61
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...
1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а) А — 1 0 1 -1 1 0 2 -2 (Ъ) А %— -2 -2 -4 -2 2 |3 0 7 0 5 0 7 0 3 (с) А %— 1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а)...
3) (9 points) For each of the following matrices Find the eigenvalues and associated eigenvectors. If possible, state the matrices P and D, such that A = PDP-1. (Hint: P is a matrix containing eigenvectors of A on its columns, and D is a diagonal matrix.) If it is not possible to find P and D, just state so. 11-133b a. A = 1 2 2 1-2 -2 -2 2 0 -1 3] b. A = [1 -4 110 0...
Problem 4 Reduce the matriz A and find A- A = (1 2 1 1 1 1 1 (3-11) by using row operations (write all corresponding E, matrices) and simultaneously apply these op- erations to the identity matrix to produce its inverse matrix. THIS MEANS: each step in your table has the form (ABE) (where * contains rows operations R R, R R + AR; or R + R), with the initial step (ABLE ] = |A77), the beginning of...