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Given the vectors v₁ = 0 2 2 nx n matrix and b is a scalar. For every row. 2 2 0 , 2/2= 2 0 2 of B, the sum of all the entries is equal to the scalar b. and 3 = 1. Determine whether the matrix A is invertible or not. and let A = [v₁ V2 V3]. Assume that B is an 2. For every row of the matrix A, the sum of all the entries is equal to 4. Prove that 4 is an eigenvalue of -8 the matrix A with the corresponding eigenvector 3. Find all the other eigenvalues and the corresponding eigenvectors for each eigenvalue.

Given the vectors v₁ = 0 2 2 nx n matrix and b is a scalar. For every row. 2 2 0 , 2/2= 2 0 2 of B, the sum of all the entries is equal to the scalar b. and 3 = 1. Determine whether the matrix A is invertible or not. and let A = [v₁ V2 V3]. Assume that B is an 2. For every row of the matrix A, the sum of all the entries is equal to 4. Prove that 4 is an eigenvalue of -8 the matrix A with the corresponding eigenvector 3. Find all the other eigenvalues and the corresponding eigenvectors for each eigenvalue.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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0 Given the vectors v₁ = 2 , 22 = and let A = [v₁ V2 V3]. Assume that B is an n x n matrix and b is a scalar. For every row of B, the sum of all the entries is equal to the scalar b. 1. Determine whether the matrix A is invertible or not. 2 2 0 and 3 = 2. For every row of the matrix A, the sum of all the entries is equal to 4. Prove that 4 is an eigenvalue of the matrix A with the corresponding eigenvector B 3. Find all the other eigenvalues and the corresponding eigenvectors for each eigenvalue. 4. Prove that b is an eigenvalue of B. 5. If B is an invertible matrix, b0, prove that 6 is an eigenvalue of B-¹.
Transcribed Image Text:0 Given the vectors v₁ = 2 , 22 = and let A = [v₁ V2 V3]. Assume that B is an n x n matrix and b is a scalar. For every row of B, the sum of all the entries is equal to the scalar b. 1. Determine whether the matrix A is invertible or not. 2 2 0 and 3 = 2. For every row of the matrix A, the sum of all the entries is equal to 4. Prove that 4 is an eigenvalue of the matrix A with the corresponding eigenvector B 3. Find all the other eigenvalues and the corresponding eigenvectors for each eigenvalue. 4. Prove that b is an eigenvalue of B. 5. If B is an invertible matrix, b0, prove that 6 is an eigenvalue of B-¹.
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