SOLUTION: Consider the matrix shown below: Find the determinant of the matrix Q.
A. -67
B. -65
C. 65
D. 67
The question is provided in the link here: https://i.imgur.com/
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Probability-and-statistics
-> SOLUTION: Consider the matrix shown below: Find the determinant of the matrix Q.
A. -67
B. -65
C. 65
D. 67
The question is provided in the link here: https://i.imgur.com/
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Question 1161541: Consider the matrix shown below: Find the determinant of the matrix Q.
A. -67
B. -65
C. 65
D. 67
The question is provided in the link here: https://i.imgur.com/IKY3rQg.png Found 2 solutions by MathLover1, greenestamps:Answer by MathLover1(20849) (Show Source):
I certainly wouldn't go to all the work that tutor @MathLover1 did to find the determinant. There is a lot of work she didn't show involved in turning the entries below the main diagonal to zeros.
For a 3x3 matrix, expanding by minors is one way to find the determinant.
Your matrix is
Expanding by minors, the determinant is
2 times the determinant of
minus 3 times the determinant of
plus 4 times the determinant of
Answer D
For larger matrices, expanding by minors is very inefficient. Here is another method for calculating the determinant of any square matrix.
(1) Create a new matrix by copying (for a 3x3 matrix) the first two columns to make a 3x5 matrix:
(2) The determinant of the original matrix is
the sum of the products of the entries in the down-to-the-right diagonals
minus
the sum of the products of the entries on the down-to-the-left diagonals:
