Consider the following matrix $A = egin{bmatrix} 7 & 3 & 1 -3 & 1 & -1 6 & 6 & 6 end{bmatrix}$. It is known that $lambda = 6$ and $lambda = 4$ are two eigenvalues of $A$; and an eigenvector corresponding to the eigenvalue $lambda = 6$ is $egin{bmatrix} 1 -1 2 end{bmatrix}$. This question has three parts. You need to choose the correct answers from the drop-down menus: Part 1: The geometric multiplicity of the eigenvalue $lambda = 4$ is [Select] Part 2: The algebraic multiplicity of the eigenvalue $lambda = 4$ is [Select]
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In other words, it is the number of linearly independent eigenvectors corresponding to that eigenvalue. We are given that the eigenvalue A = 6 has only one eigenvector, so the geometric multiplicity of A is 1. Part 2: The algebraic multiplicity of the eigenvalue Show more…
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