Let A = [111] 1 2 3. Write A as the product of elementary matrices. (1...
(2 points) Let (2 points) Let A=[% ] () Write A as a product of 4 elementary matrices: A (ii) Write A-' as a product of 4 elementary matrices: - THE -1
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
2-1 1 Write M1 0as a product of elementary matrices and find the inverse of M.
Show that is invertible by representing A as a product of elementary matrices. Then, represent A^-1 as a product of elementary matrices ГО 0 5 tA = 0 1 0 1 -3 00
9. s: ['o] Write s' as the product of elementary matrices, that is, matrices from the identity matrix through a single row are obtained that operation
2. Write the product of a sequence of elementary matrices which equals the given non-singular matrix: [ 11 2 3 3. Given the matrix A = 01 - write the matrix of minors of A, the matrix of cofactors of A, the adjoint 12 2 2 matrix of A, and use the adjoint of A, to write the inverse of A. 4. Determine whether the set of vectors is linearly dependent or linearly independent. Justify your answer. 13
a) b) hufi 2 1 Wait (3 marks) Let A = 1. Write A-1 as a product of elementary matrices. Show your work. 1 -1] [ 1 0 1] - (3 marks) Let A = -14 2 1 . Determine all values of q for which A is nonsingular. IO 1 q
1 Let A = (4 22 a) Find elementary matrices E, Er Ez - such that 2 E3 E₂E, A = I b) Find A
1. The matrices A and C are row equivalent. Find the elementary matrices such that C = E,E,E,A. 3 2 1 -4 -6 0 1 7 2 1 2 1 0 5 3 0 2 -2 5 9 6 -3 6 3 3 2 1 -4