6. Find an elementary matrix E such that EA-C 2 4 [1 A=0 1-1 -3] 21...
Question 1 [10 points] Given the following matrices A and B, find an elementary matrix E such that B- EA You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrbx. 4 6-6 0 7 0 5-2 -4 -7 1-10 -4 6-6 0 4 -4 9-3 4 -4 9-3 o 0 0 E- 0 0 0
1. Algebra: Why are all these determinants zero? 3 -1 6 21 1 0 0 0 1 -2 3 -4 1 3 1 2 7 -1 2 2 1 3 5 2 3 4 5 (a) 1 1 1 1 1; (b) 2 5 2; (c) 3 0 1 -73 (d) 3 1 7 11 3 7 3 3 -1 6 21 5 2 6 10 3 3 3 3 2. Algebra: - la b c Given that d e...
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
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.
a. The elementary matrix ?1E1 multiplies the first row of A by 1/6.b. The elementary matrix ?2E2 multiplies the second row of A by -4.c. The elementary matrix ?3E3 switches the first and second rows of A.d. The elementary matrix ?4E4 adds 6 times the first row of A to the second row of A.e. The elementary matrix ?5E5 multiplies the second row of B by 1/3.f. The elementary matrix ?6E6 multiplies the third row of B by -4.g. The elementary matrix ?7E7 switches the first and third rows of B.h. The elementary matrix ?8E8 adds...
(1 point) Assume that A is a matrix with three rows. Find the elementary matrix E such that E A gives the matrix resulting from A after the given row operation is performed. R2 R3 E=
1. Find the Jordan canonical forms of the following matrices 0 0 -1 (c) 7 6-3 (b) 2 3 2 1 0 4 0 1 -3 -10-8-6-4 0 -3 1 2 0-1 0 0 0 (d) 2 2 21-1 2 (e) 0-2-5-3 -2 0 6 85 4 0 -5 3-3 -2-3 4 1. Find the Jordan canonical forms of the following matrices 0 0 -1 (c) 7 6-3 (b) 2 3 2 1 0 4 0 1 -3 -10-8-6-4 0...
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
HW10P5 (10 points) Let A be the matrix A =13 5 0 (3 pts) Find the elementary matrices that perform the following row operations in sequence: a. 21 * 2 2. E31 : R3 R1R3 b. (3 pts) Show that the elementary matrices you found in (a) can be used as elimination matrices to determine the upper triangular, U, matrix of A. (4 pts) Find the lower triangular, L, matrix that verifies A C. = LU.
6. Find the determinant of the following matrix using elementary row operations. (Turn the elements above the main diagonal into zeros to have the least amount of calculations.) (10 points) -1 -9 0 -2 -4 -2 -2 4 3 -1 -1 4 3 2 1