40 lines
2.0 KiB
Markdown
40 lines
2.0 KiB
Markdown
---
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title: Determinant of a Matrix
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---
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## Determinant of a Matrix
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<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds -->
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The elements of a square matrix can be used to compute a special value called the determinant. It is denoted by det(A) or |A|. The determinant is only defined for a square matrix, i.e a matrix with identical number of rows and columns.
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The determinant of a 2x2 matrix is the simplest case(a 1x1 matrix is just the number itself).
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It is found by multiplying the opposite corners and subtracting them.
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Subsequent square matrices are just extensions of a 2x2 matrix and can be easily found by reducing them recursively as 2x2 matrices. The determinant of a 3x3 matrix is given below.
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<img src= http://www.statisticslectures.com/images/third1.gif width='300' height='100'>
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The steps to find the determinant for a 3x3 matrix are:
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- Choose a row or column to go along (say the 1st row)
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- Multiply 'a' by the 2x2 determinant formed without a's row or column.
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- Next do the same with b. Here make sure to multiply this value by -1. You will need to multiply -1 to every alternate element in the row.
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- Continue this till you do this for all elements in the row.
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- Simplify the expression by finding the individual 2x2 determinants
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- The value you obtain is the final value of the determinant of the matrix.
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This method can similarly be applied to any nxn square matrix by breking it down into basic 2x2 matrices and finding their determinants.
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Exercise - Try finding the determinant of the following 3x3 matrix
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<img src="https://cdn.kastatic.org/ka-exercise-screenshots/matrix_determinant_3x3_256.png">
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Answer = 27
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#### More Information:
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<!-- Please add any articles you think might be helpful to read before writing the article -->
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https://en.wikipedia.org/wiki/Determinant
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https://mathinsight.org/determinant_matrix
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