Determinants - Marmara Üniversitesi Bilişim Merkezimimoza.marmara.edu.tr/~cem/LA/Linear2.pdf ·...
Transcript of Determinants - Marmara Üniversitesi Bilişim Merkezimimoza.marmara.edu.tr/~cem/LA/Linear2.pdf ·...
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Determinants
we will study “determinants” or, more precisely, “determinant functions.”
• Determinants by Cofactor Expansion
• Evaluating Determinants by Row Reduction
• Properties of Determinants; Cramer's Rule
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Minors and Cofactors
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![Page 5: Determinants - Marmara Üniversitesi Bilişim Merkezimimoza.marmara.edu.tr/~cem/LA/Linear2.pdf · 2018-12-24 · where A] is the matrix obtained by replacing the entries in thejth](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed7043462136e72fb7bacfa/html5/thumbnails/5.jpg)
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Each of last four equations is called a cofactor expansion of det[A]. In each cofactor expansion the entries and cofactors all come from the same row or same column of A.
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Definition of a General Determinant
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Cofactor Expansion Along the First Column
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Evaluating Determinants by Row Reduction
• how to evaluate a determinant by reducing the associated matrix to row echelon form.
• In general, this method requires less computation than cofactor expansion
• hence is the method of choice for large matrices.
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we can put A in lower triangular form in one step by adding −3 times the first column to the fourth to obtain
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Properties of Determinants; Cramer's Rule
but!
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Determinant of a Matrix Product
if A and B are square matrices of the same size, then
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find the values of k for which A is invertible.
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