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LINEAR ALGEBRA
What are the eigenvalues of the matrix 2-31 1 -2 1 What is the...
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 eige...
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...
Linear Algebra Problem! Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose...
Linear Algebra Problem!
Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose Jordan Canonical form is given by ON OON JODODD JODOC JOOD 000000 E C6,6 ] O O O O O As we gradually give you more and more information about A below, fill in the blanks in J (and explain how you know the filled in values are correct). You may choose to order the Jordan blocks however you wish. Note: during the interview,...
True or false. Please justify why true or why false also (I) A square matrix with...
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...
(1 point) The linear transformation T: R4 R4 below is diagonalizable. T(x,y,z,w) = (x – -...
(1 point) The linear transformation T: R4 R4 below is diagonalizable. T(x,y,z,w) = (x – - (2x + y), -z, 2 – 3w Compute the following. (Click to open and close sections below). (A) Characteristic Polynomial Compute the characteristic polynomial (as a function of t). A(t) = (B) Roots and Multiplicities Find the roots of A(t) and their algebraic multiplicities. Root Multiplicity t= t= t= t= (Leave any unneeded answer spaces blank.) (C) Eigenvalues and Eigenspaces Find the eigenvalues and...
Need Help ASAP!!!! Subject: Linear Algebra (a) Let A= r 7 T 5 2 4 0...
Need Help ASAP!!!!
Subject: Linear Algebra
(a) Let A= r 7 T 5 2 4 0 1 i. Compute det A in terms of r. ii. Find all value(s) of z such that A is NOT invertible. (b) Let the characteristic polynomial of a matrix B be – 23 +22 +6%. i. Find the size of B. ii. Find all the eigenvalues of B including multiplicity. iii. Find the determinant of B.
Let A be an n x n matrix. Then we know the following facts: 1) IfR"...
Let A be an n x n matrix. Then we know the following facts: 1) IfR" has a basis of eigenvectors corresponding to the matrix A, then we can factor the matrix as A = PDP-1 2) If ) is an eigenvalue with algebraic multiplicity equal to k > 1, then the dimension of the A-eigenspace is less than or equal to k. Then if the n x n matrix A has n distinct eigenvalues it can always be factored...
Find the eigenvalues and their eigenvectors and eigenspace for each matrix listed below. If the algebraic...
Find the eigenvalues and their eigenvectors and eigenspace for
each matrix listed
below. If the algebraic multiplicity of a eigenvalue is greater
than one, nd the
geometric multiplicity as well for that eigenvalue. (There are C
and D).
3
linear algebra Find the characteristic equation of A, the eigenvalues of A, and a basis for...
linear algebra
Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. A= - -8 1 3 0 1 1 0 0 4 (a) the characteristic equation of A (b) the eigenvalues of A (Enter your answers from smallest to largest.) (11, 12, 13) = ( ]) (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of 11 basis for the eigenspace of 12 basis...
92 (a) The matrix A= 2 -5 -4 has an eigenvalue 2 -4 -5 Two of...
92 (a) The matrix A= 2 -5 -4 has an eigenvalue 2 -4 -5 Two of the entries of A are replaced by I, y so that it will not be convenient to find the eigenvalues by an application. 5 An eigenvector of A corresponding to the eigenvalue is 1 Find the value of and enter your answer in the box below. X= Number (b) Suppose that characteristic equation of a 8 x 8 matrix M is (1 - 2)4...
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5...
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5 0 1 1 For credit, you have to factor the polynomial and show work for each step. B In the following, use complex numbers if necessary. For each of the following matrices: • compute the characteristic polynomial; • list all the eigenvalues (possibly complex) with their algebraic multiplicity; • for each eigenvalue, find a basis (possibly complex) of the corresponding eigenspace, and write the...
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...
Linear Algebra Problem!
Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose Jordan Canonical form is given by ON OON JODODD JODOC JOOD 000000 E C6,6 ] O O O O O As we gradually give you more and more information about A below, fill in the blanks in J (and explain how you know the filled in values are correct). You may choose to order the Jordan blocks however you wish. Note: during the interview,...
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...
(1 point) The linear transformation T: R4 R4 below is diagonalizable. T(x,y,z,w) = (x – - (2x + y), -z, 2 – 3w Compute the following. (Click to open and close sections below). (A) Characteristic Polynomial Compute the characteristic polynomial (as a function of t). A(t) = (B) Roots and Multiplicities Find the roots of A(t) and their algebraic multiplicities. Root Multiplicity t= t= t= t= (Leave any unneeded answer spaces blank.) (C) Eigenvalues and Eigenspaces Find the eigenvalues and...
Need Help ASAP!!!!
Subject: Linear Algebra
(a) Let A= r 7 T 5 2 4 0 1 i. Compute det A in terms of r. ii. Find all value(s) of z such that A is NOT invertible. (b) Let the characteristic polynomial of a matrix B be – 23 +22 +6%. i. Find the size of B. ii. Find all the eigenvalues of B including multiplicity. iii. Find the determinant of B.
Let A be an n x n matrix. Then we know the following facts: 1) IfR" has a basis of eigenvectors corresponding to the matrix A, then we can factor the matrix as A = PDP-1 2) If ) is an eigenvalue with algebraic multiplicity equal to k > 1, then the dimension of the A-eigenspace is less than or equal to k. Then if the n x n matrix A has n distinct eigenvalues it can always be factored...
Find the eigenvalues and their eigenvectors and eigenspace for
each matrix listed
below. If the algebraic multiplicity of a eigenvalue is greater
than one, nd the
geometric multiplicity as well for that eigenvalue. (There are C
and D).
3
linear algebra
Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. A= - -8 1 3 0 1 1 0 0 4 (a) the characteristic equation of A (b) the eigenvalues of A (Enter your answers from smallest to largest.) (11, 12, 13) = ( ]) (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of 11 basis for the eigenspace of 12 basis...
92 (a) The matrix A= 2 -5 -4 has an eigenvalue 2 -4 -5 Two of the entries of A are replaced by I, y so that it will not be convenient to find the eigenvalues by an application. 5 An eigenvector of A corresponding to the eigenvalue is 1 Find the value of and enter your answer in the box below. X= Number (b) Suppose that characteristic equation of a 8 x 8 matrix M is (1 - 2)4...
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5 0 1 1 For credit, you have to factor the polynomial and show work for each step. B In the following, use complex numbers if necessary. For each of the following matrices: • compute the characteristic polynomial; • list all the eigenvalues (possibly complex) with their algebraic multiplicity; • for each eigenvalue, find a basis (possibly complex) of the corresponding eigenspace, and write the...
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