(a) To Show:
Given information:
Concept used:
Transpose of matrix means row and column of matrix gets interchanged.
Proof:
So, we get the matrix
We will show that
We will simplify the vector
So, we get
Conclusion:
(b) To show:
If
Given information:
Concept used:
Transpose of matrix means row and column of matrix gets interchanged.
Proof:
So, we get the matrix
We will simplify the vector
So, we get
Conclusion:
If
(c) To determine:
Find three independent eigenvectors of
Eigenvectors as
Given information:
Concept used:
Transpose of matrix means row and column of matrix gets interchanged.
Proof:
So, we get the matrix
To get eigenvalues, we will solve the equation
The above condition gives the following equation
As equation
So by choosing different values of these variables we get the following solutions.
So, we get the eigenvectors as
Conclusion:
Eigenvectors as
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Introduction to Linear Algebra, Fifth Edition
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