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Row operation properties of determinants and finding determinants via echelon form
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Row operation properties of determinants and finding determinants via echelon form
19:40
About this lesson
• Adding/Subtracting Rows \(\)→\(\) det \(B=\) det \(A\)
• Interchanging rows \(\)→\(\) det \(B=-\) det \(A\)
• Multiplying rows \(\)→\(\) det \(B=k\; \cdot\) det \(A\)
• Triangular Matrices
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Video 1 of 11
Row operation properties of determinants and finding determinants via echelon form
20 min
• Selected
Transpose, invertibility, and multiplicative properties of determinants
9 min
Using determinants to test linear independence of columns
2 min
Computing a 3x3 determinant using row reduction to echelon form
7 min
Factoring a scalar from a row to evaluate a determinant
2 min
Using row operations and scalar factoring to find a determinant
3 min
Showing det(A) equals det(A transpose) for a 2x2 matrix
3 min
Showing det(AB) equals det(A) times det(B) for 2x2 matrices
5 min
Using determinants to test linear independence of vectors
12 min
Proving det(A inverse) equals 1 over det(A)
6 min
Proving det(A) = 0 when two rows of a square matrix are identical
6 min