Elementary Linear Algebra 1. Let A be a square matrix such that detal - A) = 112 - 6211 +9210 a.) (3 points) What is the size of A? b.) (4 points) Is A invertible? Why or why not? c.) (3 points) How many eigenspaces does A have?
Let A be a square matrix such that det(AI – A) = 212 – 6211 + 9210 (3 points) What is the size of A? (4 points) Is A invertible? Why or why not? I (3 points) How many eigenspaces does A have?
Let A be a square matrix such that det(al – A) = 212 – 6211 + 9210. What is the size of A? Is A invertible? Why or why not? How many eigenspaces does A have?
1. Let A be a square matrix such that detal - A) = 112 - 6/11 + 9210 a.) (3 points) What is the size of A? b.) (4 points) Is A invertible? Why or why not? c.) (3 points) How many eigenspaces does A have?
linear algebra 1. Let A be a square matrix with characteristic polynomial 13 – 912 + 181 = 0. (a) What is the size of A? (b) Is A invertible? Why or why not? (C) How many cigenspaces does A have?
True or false. Please justify why true or why false also (I) A square matrix with the characteristic polynomial 14 – 413 +212 – +3 is invertible. [ 23] (II) Matrix in Z5 has two distinct eigenvalues. 1 4 (III) Similar matrices have the same eigenspaces for the corresponding eigenvalues. (IV) There exists a matrix A with eigenvalue 5 whose algebraic multiplicity is 2 and geo- metric multiplicity is 3. (V) Two diagonal matrices D1 and D2 are similar if...
Problem 3. Give the definitions of an invertible square matrix and of the inverse of Let A be a square matrix. List at least five conditions that are equivalent to A being Prove that the inverse of a square matrix is unique if it exists. a square matrix. invertible. Problem 3. Give the definitions of an invertible square matrix and of the inverse of Let A be a square matrix. List at least five conditions that are equivalent to A...
Let A and B be square matrices and P be an invertible matrix. If A- PBP-,show that A and B have the same determinant. Let A and B be square matrices and P be an invertible matrix. If A- PBP-,show that A and B have the same determinant.
4. Let A be a square matrix. Assume that Ak = 0 for some positive integer k. Then prove that a) 1-A is is invertible b) (1 - A)-1 = 1 + A + A + A + ................ + Ak-1 (This question is printed wrong in the text book, 10th edition. If you have this book, correct it)
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...