Answer: The required characteristic polynomial of the given matrix A is
Step-by-step explanation: We are given to find the characteristic polynomial of the following 3 × 3 matrix A with unknown variable x :
We know that
for any square matrix M, the characteristic polynomial is given by
where I is an identity matrix of same order as M.
Therefore, the characteristic polynomial of matrix A is
Thus, the required characteristic polynomial of the given matrix A is
Tthe inequality that describes this graph is y ≤ 1/3x - 4/3
<h3>How to determine the linear inequality represented by the graph?</h3>The graph that completes the question is added as an attachment
From the attached graph, we have the following points
(0, -1.3) and (3, -0.3)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (-0.3 + 1.3)/(3 - 0)
Evaluate
m = 1/3
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 1/3(x - 0) - 1.3
Evaluate
y = 1/3x - 4/3
From the graph, we have the following highlights:
The first highlight above implies, the inequality can be any of ≥ and ≤
While the second highlight above implies, the inequality is ≤
Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3
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