To prove: When the entire first column is same as that of third column of a 3 by 3 determinant its value is 0.
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,
Recall that for the matrix of order
The determinant is given as
Compute it,
Hence, it is proved that when the entire first column is same as that of third column of a 3 by 3 determinant its value is 0.
Chapter 11 Solutions
Precalculus
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