To evaluate the other four determinant having consecutive integers using graphing utility and to derive a conjecture based on the results; verify the conjecture.
Answer to Problem 84E
The properties of the determinant define that, if a column can be written as a linear combination of the other columns, the value of the determinant is zero. So, the determinant of the matrix having entries as consecutive integers is obtained as zero.
Explanation of Solution
Given information :
An example of matrix in which entries are conjecture base is given.
Let, the four-determinant having consecutive integers be,
Using the graphing utility, the value of the above determinant are obtained as zeros.
According to the properties of the determinant, if a column can be written as a linear combination of the other columns, the value of the determinant is zero.
Therefore,
The determinant of the matrix having entries as consecutive integers is obtained as zero.
Chapter 7 Solutions
Precalculus with Limits: A Graphing Approach
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