To show: When the first and third column of a 3 by 3 determinant are interchanged the value of the new determinant is
Explanation of Solution
Given information:
The determinant of a 3 by 3 matrix.
Formula used:
For the matrix of order
The determinant is given as
Proof:
Consider a 3 by 3 matrix say,
Now, denote the determinant of the above matrix as,
Compute it,
Now, interchange the column 1 and 3 of the original matrix, so new matrix is
Now, denote the determinant of the above matrix as,
Compute it,
Observe that,
Hence, it is shown that when the first and third column of a 3 by 3 determinant are interchanged the value of the new determinant is
Chapter 11 Solutions
Precalculus
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