2. Write the product of a sequence of elementary matrices which equals the given non-singular matrix:...
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
Prove that type 1 elementary matrix is a product of type 2 and 3 elementary matrices
Find the eigenvalues of the given matrices Property 2 A matrix is singular if and only if it has a zero eigenvalue 17. 21] 4t 11. Verify Property 2 for 6 A= 3 -1 2 21 7
2-1 1 Write M1 0as a product of elementary matrices and find the inverse of M.
Let A = [111] 1 2 3. Write A as the product of elementary matrices. (1 4 5
2 -25 4)[10+10+10pts.) a) Find the eigenvalues and the corresponding eigenvectors of the matrix A = b) Find the projection of the vector 7 = (1, 3, 5) on the vector i = (2,0,1). c) Determine whether the given set of vectors are linearly independent or linearly dependent in R" i) {(2,-1,5), (1,3,-4), (-3,-9,12) } ii) {(1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1) }
Please solve using matrices and not equations. Thanks. 2. Given the columns of the matrix u v w 0 1 2 0-1 0 0 r S t -1 021 01 0 For each of the sets of vectors given below, answer the following questions: (i) Is the set linearly independent? 1 Does the set span (iii Does the vector a- (a) S (r, s, t, u) (b) T fr,t, 0, u) (c) U = {r, t, w, u, v} (3,2,1,5)...
18] 2. Determine whether the given set is a basis for all 2x2 matrices - [ 6 7-] [! ( 1 [ ] [ ] [ [8] 3. Find the inverse of the matrix (if possible). I a b where ab #0 [ 2 -1 1 1 2 11 [2 2 2 a. Solve the following system of linear equations by using the inverse of a matrix. Sr -y = 1 13. +y = 7 -y +z = 1 c....
Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2 -1 01 0 - 1 3 1 1 -6 2 1 - 12 Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) O A. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that...
4) a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: *1 + 2y, - 2 = 5 4x1 +9y1 - 32 = 8 (5x + 12y - 321 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to 1's). Reduce from left to right through the columns and from the pivot entry down...