Linear Algebra Thank you 6-Prove that 0 is an eigenvalue of a matrix A if and...
linear algebra (1 point) Prove that if X+0 is an eigenvalue of an invertible matrix A, then is an eigenvalue of A! Proof: Suppose v is an eigenvector of eigenvalue then Au=du. Since A is invertible, we can multiply both sides of Au= du by 50 Az = Azj. This implies that . Since 1 + 0 we obtain that Thus – is an eigenvalue of A-? A.D=AU B. A=X co=A D. X-A7 = E. A- F. Av= < P...
question about linear algebra 1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as an eigenvalue with algebraic multiplicity 1. The eigenvalue -2 has an associated eigenvector The eigenvalue 4 has an associated eigenvector 1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as...
Help on this question of Linear Algebra, thanks. Let A be a square matrix. Prove that A is invertible if and only if det(A) +0.
Linear algebra 6. Prove that if a real matrix An xn satisfies A100-Inxn (the identity matrix), then det(A) ±1. 6. Prove that if a real matrix An xn satisfies A100-Inxn (the identity matrix), then det(A) ±1.
Linear algebra, please have a legible answer. Thank you. 6. [10 points) Find a matrix that diagonalizes A and determine P-1AP.
linear algebra Explain why the matrix is not diagonalizable. A= 8 0 0 1 8 0 0 0 8 O A is not diagonalizable because it only has one distinct eigenvalue. O A is not diagonalizable because it only has two distinct eigenvalues. O A is not diagonalizable because it only has one linearly independent eigenvector. O A is not diagonalizable because it only has two linearly independent eigenvectors.
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.
Linear Algebra 4. Prove that the eigenvalues of A and AT are identical. 5. Prove that the eigenvalues of a diagonal matrix are equal to the diagonal elements. 6. Consider the matrix ompute the eigenvalues and eigenvectors of A, A-,
5. A is a nonsingular matrix (that is A-exists) and suppose is an eigenvalue of A with associated eigenvector K. 5.1 Prove that 1 70. (Hint: Suppose that i = 0.) 5.2 Show that is an eigenvalue of A-- with corresponding eigenvector K. 5.3 Show that 12 is an eigenvalue of A² with corresponding eigenvector K. (This statement is true even if A is singular.)
Linear Algebra Please show details. Thank you. 36. Proof Prove that if A and B are similar matrices and A is nonsingular, then B is also nonsingular and A-1 and B-1 are similar matrices.