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): You can put this solution on YOUR website!

your matrix:

Eliminate elements in the 1st column under the 1st element


Multiply the main diagonal elements
Δ =

answer: D.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


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:


minus


=


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