Find the inverse of the matrix, applying elementary
operations by lines
Find the inverse of the matrix, applying elementary operations by lines
4. Use elementary row operations (Gauss-Jordan method) to find the inverse of the matrix (if it exists). If the inverse does not exist, explain why. 1 0-1 A:0 1 2 0 -1 2us 0P 0 Determine whether v is in span(ui, u2, us). Write v as a linear combination of ui, u2, and us if it is in span(u1, u2, u3). If v is not in span(ui, u2, u3), state why. span(ui,u2,us). If v is not in span(ui,u^, us), state...
Find the inverse of the elementary matrix E1 E2 E3 E4 and show the step 1 2 3 4
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
Consider some elementary row operation. Show that the corresponding elementary matrix is obtained by applying this row operation to the identity matrix. How do we know what size of identity matrix to use?
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT. Give a proof that if A has an inverse, then so does AT. (c) Let A be a 3 x 3 matrix that can be transformed into the identity matrix by perform ing the following three row operations in the given order: R2 x 3, Ri R3, R3+2R1 (i) Write down the elementary...
1. A Western student paid someone $250 to find elementary row operations transforming the augmented matrix (A|b) to the matrix (1 6 0 -3 010) 0 0 1 4 0 7 (RS) = 0 0 0 0 15 10 0 0 0 0 0 The Western student has no idea what this means, but you do. Assuming the field is R, describe the solution set to the system of linear equations (A[6] (equivalently, the matrix equation AX = b). Your...
Find the inverse of the matrix using row operations: 1 4 -1 1 A= -1 2 -3 6 -1
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
0 points) Matrix Operations - Inverse of a Matrix This problem is related to Problem 5.21 in the text. Given the matrix I 2 -3 1 ] , -1 1 -1 1 -1 0 a) does the inverse of the matrix exist? Your answer is (input Yes or No): b) if your answer is Yes, write the inverse here; if the answer is NO, enter all zeros here:
(b) Determine the inverse of the following matrix using elementary row operations 0 1 [ 3 C = -1 2 5 O-11VIMU (50 marks) Given the vector field F = x2i +2xj + z?k and the closed curve is a square with vertices at (0,0,3), (1, 0, 3), (1, 1, 3), and (0, 1,3), verify Stoke's Theorem (a) 5. (50 marks) Use the Gauss-Seidel iterative technique to find approximate solutions to (b) 6 +2x3 10x1 +3x4 11x2 X3 11 x4...