Determinant of 4x4 Matrix: Is the Method Used in the Video Accurate?

In summary, the method shown in the video for finding the determinant does not work for a 4x4 matrix. The correct answer for the determinant of the given matrix is zero, according to an online calculator and the lecturer's instructions.
  • #1
ZedCar
354
1

Homework Statement



I was using the method shown in the following video;


to find the determinant for the following 4x4 matrix

1 -2 3 -4
5 6 -7 8
-9 -10 11 -12
-13 14 -15 16



The Attempt at a Solution



I was therefore expanding this out by using the first three columns set to the right of this matrix.

Is this the correct thing to do if using this method?

I get an answer of -3264

Though when I use this online determinant calculator
http://www.bluebit.gr/matrix-calculator/
it provides an answer of 0
 
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  • #2
Apparently this method simply doesn't work for a 4x4 matrix.
And I've been told the correct answer is zero.

Just that our lecturer stated when finding the determinant using this method;

nxn determinant
add n-1 columns

So I thought by this he meant doing what I had done above.
 

1. What is a determinant of a 4x4 matrix?

The determinant of a 4x4 matrix is a value that can be calculated from the elements of the matrix. It is a unique number that represents certain properties of the matrix, such as whether it is invertible or singular.

2. How do you calculate the determinant of a 4x4 matrix?

To calculate the determinant of a 4x4 matrix, you can use the Laplace expansion method or use a calculator or computer program. The Laplace expansion method involves breaking down the matrix into smaller matrices and using certain formulas to find the determinant.

3. What is the significance of the determinant of a 4x4 matrix?

The determinant of a 4x4 matrix has several important uses in mathematics, physics, and engineering. It can be used to solve systems of linear equations, find inverses of matrices, and calculate areas and volumes in geometry.

4. What does a determinant of 0 mean for a 4x4 matrix?

If the determinant of a 4x4 matrix is 0, it means that the matrix is singular and does not have an inverse. This also means that the matrix is not full rank and has linearly dependent rows or columns.

5. Can the determinant of a 4x4 matrix be negative?

Yes, the determinant of a 4x4 matrix can be negative. The sign of the determinant depends on the number of row and column swaps required to put the matrix into upper triangular form. A negative determinant indicates an odd number of swaps, while a positive determinant indicates an even number of swaps.

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