How to calculate the determinant?

Thread starter kakarotyjn
Start date Apr 9, 2011
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Determinant

In summary, a determinant is a single number that represents the scaling factor of a square matrix and provides information about its invertibility and solutions to linear equations. To calculate the determinant of a 2x2 matrix, you multiply the numbers in the main diagonal and subtract the product of the numbers in the other diagonal. The formula for a 3x3 matrix is a(ei-fh) - b(di-fg) + c(dh-eg). The determinant can be negative, depending on the number of row swaps needed to get the matrix into upper triangular form. Some applications of calculating the determinant include solving systems of linear equations, finding areas and volumes of geometric shapes, and determining the stability of systems in physics and engineering.

Apr 9, 2011

kakarotyjn

the problem is in the image

Last edited: Apr 9, 2011

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Apr 9, 2011

Chantry

All I see is an image to a chinese chat program called qq.

Apr 9, 2011

kakarotyjn

Sorry for that,now I edit it and upload the picture.

Apr 10, 2011

kakarotyjn

sorry,the second picture is rotated in the wrong direction,I change it right.

1. What is a determinant?

The determinant is a mathematical concept used to determine the properties of a square matrix. It is a single number that represents the scaling factor of the matrix and can provide information about the matrix's invertibility and its solutions to linear equations.

2. How do I calculate the determinant of a 2x2 matrix?

To calculate the determinant of a 2x2 matrix, you simply multiply the numbers in the main diagonal (top left to bottom right) and subtract the product of the numbers in the other diagonal (top right to bottom left). For example, the determinant of the matrix [a b; c d] is ad - bc.

3. What is the formula for calculating the determinant of a 3x3 matrix?

The formula for calculating the determinant of a 3x3 matrix is:a(ei-fh) - b(di-fg) + c(dh-eg), where a, b, and c are the first row of the matrix, d, e, and f are the second row, and g, h, and i are the third row.

4. Can the determinant be negative?

Yes, the determinant can be negative. The sign of the determinant depends on the number of row swaps needed to get the matrix into upper triangular form. If an odd number of swaps are needed, the determinant will be negative, and if an even number of swaps are needed, the determinant will be positive.

5. What are some applications of calculating the determinant?

Calculating the determinant is useful in many areas of mathematics and science, including linear algebra, calculus, physics, and engineering. It is used to solve systems of linear equations, find areas and volumes of geometric shapes, and determine the stability of systems in physics and engineering.