Matrices T2 Flashcards
what is an upper triangular matrix
a matrix with all non zero entries above or on the main diagonal
what are matrix determinant properties?
- if there’s a row or column of all zeroes the det A = 0
- If a row of A is a multiple of some other row of A, then det A = 0. Similar for columns.
- if A is an upper triangular matrix the determinant is the product along the diagonal
what are the elementary row operations
- add one row to another
- multiply a row by a non zero scalar
-add multiples of a row to another row - swapping rows
what does it mean for a matrix too be in reduced row echelon form
A matrix in REF is further said to be in reduced row ech- elon form (RREF), if all leading entries are 1 and if each leading entry is the only non-zero entry in its column.
what is the rank of a matrix
The rank of a matrix is the number of non-zero rows in its REF.
if the REF of the augmented matrix has a row of zeros on the A-side, but the corresponding RHS entry is different from zero, then the system has no solutions
if the REF of the augmented matrix has a row of zeros on the A-side, but the corresponding RHS entry is different from zero, then the system has no solutions
what is an eigenvalue and an eigenvector
EigenvaluesandEigenvectors. Let A be a n×n square matrix. A scalar λ ∈ R is called an eigenvalue of A, if there exists a n-vector v ̸= 0 with
A⃗v = λ⃗v.
Such a vector ⃗v is called an eigenvector of A.