To find: the determinants of four matrices in which the entries are consecutive integers using graphing utility, An example of such matrix is shown below. Make a conjecture based on the results. Then verify conjecture.
Answer to Problem 86E
The determinant of any consecutive integer’s matrix is equal to zero.
Explanation of Solution
Given information: Given consecutive integers matrix is show below.
Formula used:
Leibniz formula;
The Leibniz formula for the determinant of a 3 × 3 matrix:
Calculation:
Given consecutive integers matrix is,
Other three consecutive integer’s matrices may be,
Using graphing utility.
So, on the bases of result conjecture is that the determinant of any consecutive integer’s matrix is equal to zero.
Verification of the conjecture,
Take another consecutive integers matrix
So, determinant of thisconsecutive integer’s matrix is zero.
Hence, conjecture is verified.
Chapter 7 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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