Matrices T2 Flashcards

1
Q

what is an upper triangular matrix

A

a matrix with all non zero entries above or on the main diagonal

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2
Q

what are matrix determinant properties?

A
  • 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
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3
Q

what are the elementary row operations

A
  • add one row to another
  • multiply a row by a non zero scalar
    -add multiples of a row to another row
  • swapping rows
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4
Q

what does it mean for a matrix too be in reduced row echelon form

A

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.

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5
Q

what is the rank of a matrix

A

The rank of a matrix is the number of non-zero rows in its REF.

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6
Q

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

A

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

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7
Q

what is an eigenvalue and an eigenvector

A

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.

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8
Q
A
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