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Chapter 5: Determinants

Terms in this set (16)

The determinant of any identity matrix:
Is 1
Interchanging two rows of a matrix...
Has the effect of changing the sign of the determinant
When the other rows of a matrix is held constant, the determinant is...
A linear function of the first row of the matrix
if two rows of a matrix are equal,
the determinant of the matrix is zero
Adding a multiple of one row to another...
Doesn't change the determinant
If the other rows of a matrix are held constant, the determinant is...
a linear function of each row of the matrix
If a matrix has a row of zeroes...
Then it's determinant is zero
If A is a triangular matrix (upper triangular or lower triangular),
Then the determinant of A is the product of the entries on the main diagonal.
If A is invertible,
det(A) ≠0.
If A is not invertible,
det(A) =0
singular
A matrix that is not invertible.
non-singular
A matrix that is invertible
If A and B are square matrices of the same size,
det(AB) = det(A)*det(B)
for a square matrix A, det(A^t)
= det(A)
if A is an nxn matrix where the first row contains a number followed by a row of zeroes, then det(A)=
a det(B)
Laplace expansion
Esesntially use linearity in the first row to write the matrix as a sum of the first row, with one column a number and the rest a string of zeroes.
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