Concept explainers
For Problems 1-6, evaluate the determinant of the given matrix
a.
To explain:
The value of the determinant of matrix
Answer to Problem 1AP
Solution:
The determinant of matrix
Explanation of Solution
Given:
The matrix
Approach:
By using the definition of determinants the value of general matrix of second order is
Calculation:
As, the value of determinant for general matrix of second order is
Then for matrix
So,
b.
The value of the determinant of matrix
Answer to Problem 1AP
Solution:
The determinant of matrix
Explanation of Solution
Given:
The matrix
Approach:
By converting the given matrix to upper triangular matrix in which the entries below diagonal elements are zero and then taking the product of diagonal elements of the equivalent matrix gives the determinant of the matrix.
Calculation:
Firstly apply the row operation as adding one third of the first row to the second row it gives
Thus,
That is,
c.
The value of the determinant of matrix
Answer to Problem 1AP
Solution:
The determinant of matrix
Explanation of Solution
Given:
The matrix
Approach:
According to cofactor expansion theorem the determinant of general second order matrix is given by
Calculation:
So, by the expansion theorem the
Thus,
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