Quiz 5 Flashcards
What is the determinant of an upper or lower triangular matrix?
The product of its diagonal elements
How do you find the determinant by minors?
Choose a row/column with the most amount of zeros. Traverse down that row/column, multiplying the resulting minor by the number which you are on. Remember the alternating positive negative pattern. Sum the determinants of the minor times their cofactors.
What is det(AB) equal to?
det(a)*det(b)
How does determinant relate to volume?
The determinant of the matrix whos columns are made of two vectors which outline an area is the area no matter how many dimensions
What is the determinant of a diagonal matrix?
The product of its diagonal elements
What is true if a matrix has a zero column or zero row?
Its determinant is 0
What is true of the transpose of a matrix as related to determinants?
det(A) = det(A^T)
What is true of a matrix B if B is the matrix A with two of its rows swapped?
det(B) = -det(A) (one negative per swap, not total)
If a matrix has linearly dependent rows/columns?
Its determinant is 0
What is true of a matrix B if B is the matrix A with one of its rows multiplied by a scalar x?
det(B) = x*det(A)
For a nxn matrix A what is true of the statement det(x*A) where x is some scalar?
det(xA) = x^ndet(A)
What is true of a matrix B if B is the matrix A with one of its rows added onto by a scalar multiple of another one of its rows?
det(B) = det(A)
