a.
To calculate: The characteristic polynomial
The polynomial is
Given Information:
The matrix is
Calculation:
Consider the given matrix,
Polynomial is defined as,
Substitute the values and find
Find the determinant.
Therefore, the obtained function is
b.
To graph: The function
The required graph is shown as below,
Given Information:
The function is
Explanation:
Consider the given information,
Find the intercept of the function by using 0 for x and 0 for y one by one.
And,
And,
The vertex is
Now, make the graph.
Therefore, the required graph is above graph.
c.
To calculate: The Eigen values of the given matrix
Eigen values are
Given Information:
The matrix is
Calculation:
Consider the given information,
Now, find the Eigen values.
And the root can be taken form the previous part (b).
Therefore, the Eigen values are
d.
To determine: The compression between determinant of the given matrix and the y -intercept.
The value of
Given Information:
The matrix is
Calculation:
Consider the given information,
Now, find the determinant.
And, the y -intercept is 13.
Therefore, the both the values are equal.
e.
To determine: The comparison between the sum of the main diagonal elements of A with the sum of the eigenvalues.
The main diagonal elements of A with the sum is equal to the sum of the eigenvalues.
Given Information:
The matrix is
Calculation:
Consider the given information,
Now, find the sum of diagonal entries of the matrix.
Refer the Eigen values form the previous part and add them.
Therefore, the both the values are equal.
Chapter 7 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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