Linear algebra#7 plss ### Linear Algebra: Basis and Eigenvalues Problems#### Problem 7**Given Matrix:**\[ A = \begin{pmatrix} 1 & -1 & 0 & 3 & -2 \\ 0 & 1 & 0 & -4 & 7 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 6 \end{pmatrix} \](A) **Find a basis for Col A**(B) **Find a basis for Nul A**---#### Problem 8**Given Matrix:**\[ \text{Let} \quad A = \begin{pmatrix} 5 & 2 \\ 2 & 8 \end{pmatrix} \]**Calculate the eigenvalues \(\lambda_1\) and \(\lambda_2\) of A, and the corresponding eigenvectors \(\mathbf{v}_1\) and \(\mathbf{v}_2\)**---### Instructions1. **Basis for the Column Space (Col A):** - The column space of matrix \(A\) (Col \( A \)) is the span of the linearly independent columns of \(A\).2. **Basis for the Null Space (Nul A):** - The null space of matrix \(A\) (Nul \(A\)) is the set of all solutions to the equation \(A\mathbf{x} = \mathbf{0}\).3. **Eigenvalues and Eigenvectors:** - Eigenvalues \(\lambda\) and eigenvectors \(\mathbf{v}\) can be found by solving the characteristic equation \(\det(A - \lambda I) = 0\). - Substitute each \(\lambda\) into the equation \((A - \lambda I)\mathbf{v} = \mathbf{0}\) to find the corresponding eigenvector \(\mathbf{v}\).### Detailed Steps and SolutionsPlease proceed with the step-by-step calculations for finding the bases for Col \( A \) and Nul \( A \), as well as the eigenvalues and eigenvectors for the given matrices.

Answered: Image /qna-images/answer/2ded1d09-b46e-4366-97a3-0898ad30ec3c.jpg

Answered: Problem 7 [1 -1 0 0 10-4 7 If A = 0010…

Problem 7 [1 -1 0 0 10-4 7 If A = 0010 6 0000 0 A) Find a basis for Col A -27 B) Find a basis for Nul A

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 3CEXP

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