4x4 determinant using upper triangular form

In summary, a 4x4 determinant using upper triangular form is a mathematical method for calculating the determinant of a 4x4 matrix. This involves arranging the elements of the matrix in an upper triangular form and multiplying the diagonal elements to find the determinant. To find the upper triangular form of a 4x4 matrix, one must use elementary row operations such as swapping rows, multiplying rows by a constant, and adding multiples of one row to another. The upper triangular form is used for calculating determinants because it simplifies the process and makes it easier to perform the necessary calculations. It can be used for matrices of different sizes, but it is limited to square matrices and can become more complex for larger matrices. Other methods may be more
  • #1
aznkid310
109
1
[SOLVED] 4x4 determinant using upper triangular form

Homework Statement



|2 0 1 4|
|3 2 -4 -2|
|2 3 -1 0|
|11 8 -4 6|


Homework Equations



Ive done this a number of times and i still can't get the answer. I ended up w/ 275, but the answer is suppose to be zero

The Attempt at a Solution



1) 2 * |1 0 0.5 2|
|3 2 -4 -2|
|2 3 -1 0|
|11 8 -4 6|

2) 2* |1 0 0.5 2|
|0 2 -5.5 -8|
|0 3 -2 -4|
|0 8 -9.5 -5|

3) (2)(2)*|1 0 0.5 2|
| 0 1 -2.75 -4|
|0 3 -2 -4|
|0 8 -9.5 -5|

4) (2)(2)*|1 0 0.5 2|
| 0 1 -2.75 -4|
|0 0 6.25 8|
|0 0 12.5 27|

5) (2)(2)(6.25)* |1 0 0.5 2|
|0 1 -2.75 -4|
|0 0 1 (32/25)|
|0 0 0 11|

Determinant = 11*2*2*6.25 = 275
 
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  • #2
aznkid310 said:
2) 2* |1 0 0.5 2|
|0 2 -5.5 -8|
|0 3 -2 -4|
|0 8 -9.5 -5|
I would double-check your last row carefully for step 2.
 
  • #3
ah i see! Thanks for pointing that out.
 

1. What is a 4x4 determinant using upper triangular form?

A 4x4 determinant using upper triangular form is a mathematical method for calculating the determinant of a 4x4 matrix. It involves arranging the elements of the matrix in an upper triangular form and then multiplying the diagonal elements to find the determinant.

2. How do you find the upper triangular form of a 4x4 matrix?

To find the upper triangular form of a 4x4 matrix, you must use elementary row operations to transform the matrix into an upper triangular form. This involves swapping rows, multiplying rows by a constant, and adding multiples of one row to another. Once the matrix is in upper triangular form, the determinant can be easily calculated.

3. Why is the upper triangular form used for calculating determinants?

The upper triangular form is used for calculating determinants because it simplifies the process and makes it easier to perform the necessary calculations. By arranging the matrix in this form, the determinant can be found by simply multiplying the diagonal elements, rather than using more complex methods such as cofactor expansion.

4. Can the upper triangular form be used for matrices of different sizes?

Yes, the upper triangular form can be used for matrices of different sizes, not just 4x4. The method involves transforming the matrix into an upper triangular form, which can be done for any square matrix. However, the size of the matrix will determine the number of calculations needed to find the upper triangular form and the determinant.

5. Are there any limitations to using the upper triangular form for finding determinants?

One limitation of using the upper triangular form is that it can only be used for square matrices. Additionally, for larger matrices, the process of finding the upper triangular form and calculating the determinant can become more time-consuming and complex. In these cases, other methods may be more efficient.

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