Section 1

Preview this deck

Geometrically, if lambda is an eigenvalue of a matrix A and x is an eigenvector of A corresponding to lambda, then multiplying x by A produces a vector lambda*x parallel to x

Front

Star 0%
Star 0%
Star 0%
Star 0%
Star 0%

0.0

0 reviews

5
0
4
0
3
0
2
0
1
0

Active users

0

All-time users

0

Favorites

0

Last updated

2 years ago

Date created

Mar 1, 2020

Cards (34)

Section 1

(34 cards)

Geometrically, if lambda is an eigenvalue of a matrix A and x is an eigenvector of A corresponding to lambda, then multiplying x by A produces a vector lambda*x parallel to x

Front

T

Back

The nullspace of a matrix A is also called the solution space of A

Front

t

Back

if an mxn matrix A is row-equivalent to an mxn matrix B then the row space of A is equivalent to the row space of B

Front

T

Back

The 0 vector

Front

is never an eigen vector, the eigen value can be 0

Back

If A and B are similar nxn matrices, then they always have the same characteristic polynomial equation

Front

T

Back

The scalar lambda is an eigenvalue of an nxn matrix A when there existsa vector x such that Ax = lambda*x

Front

F

Back

To find the eigenvalue(s) of an nxn matrix A, you can solve the characteristic equation det(lambda*I - A) = 0

Front

T

Back

The column space of a matrix A is equal to the row space of At

Front

T

Back

for unique eigen values,

Front

the eigen vectors are linearly independent

Back

If an mxn matrix B can be obtained from elementary row operations on an mxn matrix A, then the column space of B is equal to the column space of A

Front

F

Back

For any 4x1 matrix X, the coordinate matrix [X]s relative to the standard basis for M4,1 is equal to X itself

Front

T

Back

Similar matrices

Front

are matrices that have the same eigen values

Back

The dot product is the only inner product that can be defined in Rn

Front

F

Back

A nonzero vector in an inner product can have a norm of zero

Front

F

Back

The zero vector 0 in Rn is defined as the additive inverse of a vector

Front

F

Back

If A is an nxnmatrix with an eigenvalue lambda, then the set of all eigenvectors of lambda is a subspace of Rn

Front

F

Back

for every eigen value there is

Front

a corresponding eigen space, the basis of which is the set of eigen vectors associated with the eigen value

Back

If dim(V) = n, then there exists a set of n-1 vectors in V that will span V

Front

F

Back

If dim(V) = n, then any set of n-1 vectors in V must be linearly independent

Front

T

Back

If dim(V) = n, then there exists a set of n+1 vectors in V that will span V

Front

T

Back

The coordinate matrix of p = 5x^2+x-3 relative to the standard basis for P2 is [p]s = [5 1 -3]T

Front

T

Back

If P is the transistion matrix from a basis B to B', then the equation P[x]B'=[x]B represents the change of basis from B to B'

Front

F

Back

The system of linear equations Ax=b is inconsistent if and only if b is in the column space of A

Front

F

Back

Any diagonal entry in a diagonal or triangular matrix

Front

is an eigen value

Back

The vector -v is called the additive identity of v

Front

F

Back

The fact that an nxn matrix A has n distinct eigenvalues does not guarantee that A is diagonalizable

Front

F

Back

If dim(V)=n, then any set of n+1 vectors in V must be linearly dependent

Front

F

Back

Two vectors in Rn are equal if and only if their corresponding components are equal

Front

T

Back

To perform the change of basis from a nonstandard basis B' to the standard basis B, the transition matrix P-1 is simply B'

Front

T

Back

If A is an mxn matrix of rank r, then the dimension of the solution space of Ax = 0 is m-r

Front

F

Back

the nullspace of a matrix A is the solution space of the homogeneous system Ax=0

Front

T

Back

If an nxn matrix A is dagonalizable, then it must have n distinct eigenvalues

Front

T

Back

If A is a diagonalizable matrix, then it has n linearly independent eigenvectors

Front

T

Back

To subtract two vectors in Rn, subtract their corresponding components

Front

T

Back