Help on this question of Linear Algebra, thanks.
Help on this question of Linear Algebra, thanks. Let A be a square matrix. Prove that...
Help on this question of Linear Algebra, thanks.
Prove that an n x n matrix A is diagonalizable if and only if A has n L.I. eigenvectors.
If anyone can help with these 3 practice problems on my linear
algebra study guide!
10. Let A be a square matrix. Prove that A is invertible if and only if det(A) +0. 11. Let W be a nonzero subspace of R”. Prove that any two bases for W contain the same number of vectors. 12. Prove that an n x n matrix A is diagonalizable if and only if A has n L.I. eigenvectors.
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?
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?
Linear Algebra question: If A, B are square matrices and AB is invertible (Inverse), prove that A and B are invertible (Inverse).
Suppose A is a square matrix such that det A4 invertible. 0. Prove that A is not Suppose that A is a square matrix such that det A" invertible and that it must have determinant 1. 1. Prove that A is Matrices whose determinant is 1 are part of a group (not just the english word, a special math term, ask if you want the deets) called the Special Linear Group, denoted SL(n) + Drag and drop your files or...
Help on this question of Linear Algebra, thanks.
Let W be a nonzero subspace of R". Prove that any two bases for W contain the same number of vectors.
Help on this question of Linear Algebra, thanks.
Let A= [ 0.7 0.1 0.3 0.9 Find P and D such that A = PDP-1, where D is a diagonal 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...
linear algebra
1 2. Let A be the 3 x 3 matrix: A= 3 3 0 -4 1-3 5 1 (a) Find det(A) by hand. (b) What can you say about the solution(s) to the linear system Az = ? A. No Solutions B. Unique Solution C. Infinitely Many Solutions (c) Is A invertible?