Linear Algebra Chapter 3.2 – Flashcards

A row replacement operation does not affect the determinant of the matrix

The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)^r, where r is the number of row interchanges made during row reduction from A to U

If the columns of A are linearly dependent, then det A = 0

det( A + B) = det A + det B

If three row interchanges are made in succession, then the new determinant equals the old determinant

The determinant of A is the product of the diagonal entries in A

If det A is zero, then two rows or two columns are the same, or a row or a column is zero

det A^-1 = (-1)det A

if B is obtained by adding a multiple of one row to another

if B is obtained from A by interchanging two rows

If B is obtained from A by multiplying one row/column by k

A is invertible if and only if

detA^T

detAB =

detA = -3 detB = 4 det 5A =

detA = -3 detB = 4 detB^T

detA = -3 detB = 4 det A^-1

detA = -3 detB = 4 det A^3

det A = -3 det B = -1 det AB

det A = -3 det B = -1 detA^T B A

det A = -3 det B = -1 det B^-1 A B