3. Find the inverse of the following matrix: (5 pts) B=11 2-3 hy row rednicing the...
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...
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
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1 0 0 2 0 0 0 0 0 0 0 0 (a) (3 pts) Let C be a matrix with rref(C) = B. Find a basis of ker(C). (b) (3 pts) Find two matrices A1 and A2 so that rref(A1) = rref(A2) im(A) # im(A2). B, and 1 (c) (5 pts) Find the matrix A with the following properties: rref(A) = B, is an...
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.
(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 B-1084 7 1o-2 3 21 6 (5+5 (b) () For any n x I vector a 0, show that a (ii) Find the g-inverse of the vector a, where a' = [1 a'a 5 2] 3 1 (a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5...
1. Write a MATLAB function that takes a matrix, a row number and a scalar as arguments and multiplies each element of the row of the matrix by the scalar returning the updated matrix. 2. Write a MATLAB function that takes a matrix, two row numbers and a scalar as arguments and returns a matrix with a linear combination of the rows. For example, if the rows passed to the function were i and j and the scalar was m,...
2. (15 pts; 8,7) Let (a) Find the inverse of the matrix X. (b) Write X-1 as a product of elementary matrices. (You only need to give the list of elementary matrices in the right order. There is no need to multiply them out. )
1) a) If A is a 4×5 matrix and B is a 5×2 matrix, then size of AB is: b) If C is a 3×4 matrix and size of DC is 2×4 matrix , then size of D is: c) True or False: If A and B are both 3 × 3 then AB = BA d) The 2 × 2 identity matrix is: I = e) Shade the region 3x + 2y > 6. f) Write the augmented matrix...
(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...
Find the inverse of the matrix using row operations: 1 4 -1 1 A= -1 2 -3 6 -1