Problem

Given the matrix A = (1−20−21−20−21), find the characteristic equation.

Answer

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Answer

Step 3: Therefore, the characteristic equation of matrix A is λ3−3λ2+4λ−1=0.

Steps

Step 1 ：Step 1: We start by finding the determinant of the matrix A−λI, where I is the identity matrix and λ is a scalar. So, A−λI=(1−λ−20−21−λ−20−21−λ).

Step 2 ：Step 2: The determinant of A−λI is (1−λ)[(1−λ)2−4]+2∗2∗2−0, which simplifies to λ3−3λ2+4λ−1.

Step 3 ：Step 3: Therefore, the characteristic equation of matrix A is λ3−3λ2+4λ−1=0.

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