3 - 12 Let A = Construct a 2x2 matrix B such that AB is the zero matrix. Use two -4 16 different nonzero columns for B. B=
4 - 16 strict a 2x2 matrix B such tha Lota = - 4. - 16). Construct a 2 . Construct a 2 x 2 matrix B such that AB is the zero matrix. Use two different nonzero columns for B. -2 81 B=0
2. Let A be any matrix and let B= AAT a. Use a 2x2 matrix A, to verify that B is symmetric. b. Write one-line proof to show that B is symmetric. Do not use part a. 3. Using Gaussian Elimination, solve the homogeneous system 2x1 + x2 – 3x3 = 0 - x2 - 4x2 + 3x3 = 0 2 1 -3 oli +3707 1-4 3lol 1-4 30
Question 10 (10 points] Construct an example of a 2x2 matrix, with one of its eigenvalues equal to -3, that is not diagonal or invertible, but is diagonalizable. 0 0 A= 0 0
Construct a nonzero matrix B such that AB is the zero matrix. Explain and justify your process. A= 2 5 -3 -1 0-1 3 2 1
[1 2 37 1. Is the matrix 1 0 1 invertible? If yes, what is its inverse? [O 2 -1 2. A matrix is called symmetric if At = A. What can you say about the shape of a symmetric matrix? Give an example of a symmetric matrix that is not a zero matrix. 3. A matrix is called anti-symmetric if A= -A. What can you say about the shape of an anti- symmetric matrix? Give an example of an...
6. [20] Let A, B e Cnxn such that A2 = A and B2 = B. Prove that if (A + B)2 = A + B, then AB is the zero matrix 0 Rnxn.
Let D be a 2x2 linear transformation matrix that transforms the vector ? = [ 1 4 ] into the vector ?? = [ 3 6 ] and transforms the vector ? = [ 2 5 ] into the vector ?? = [ 0 9 ]. Analyze the linear transformation matrix D by doing the following: Let S be a square with side length 2, located in the xy-plane. The matrix D transforms the vertices of S into the vertices...
three small problem!!!!! Problem 7: (9 total points) Let A 11 0 -1 2 1 -1 3 -1 0 = 1 | -2 1 4 -13 3 -1 -5 1 -6 a) Find a basis for ker A. b) Find a 5 x 5 matrix M with rank 2 such that AM = 0, where is the 4 x 5 zero matrix. is the 4 x 5 zero matrix. Prove c) Suppose that B is a 5 x 5 matrix...
Matrix Methods/Linear Algebra: Please show all work and justify the answer! 4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(A”)? (d) (4 points) What is det(A-")? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of...