Question 1

Find all values of 
   so that rank 
   
, where

Accepted Answer

The answer of Find all values of 
  ...

Question 2

If 
   and 
   
, then 
   is a 
   matrix.

Accepted Answer

A) True 
 B)False

Question 3

If B is a basis for a given subspace, and u is in span (B) with 
   
, then 
   
.

Accepted Answer

A) True 
 B)False

Question 4

Find the change of basis matrix from B1 to B2.

Accepted Answer

Question 5

Determine the null space of

Accepted Answer

The answer of Determine the null space of
  ...

Question 6

If B is a basis, then 
   for all scalars 
   
, 
   and all vectors 
   
, 
   in span (B).

Accepted Answer

A) True 
 B)False

Question 7

Let A be an 
   matrix, and B an 
   matrix. Then the null space of B is a subspace of the null space of AB.

Accepted Answer

A) True 
 B)False

Question 8

By forming matrix columns, find a basis for the given subspace S and give the dimension of S, where

Accepted Answer

Basis: 
 @#IMG-DLM&

Question 9

Find a basis for the null space of the given matrix A and give 
   
.

Accepted Answer

The answer of Find a basis for the null space...

Question 10

Determine the null space of

Accepted Answer

The answer of Determine the null space of
  ...

Question 11

Expand the given set to form a basis for R4.

Accepted Answer

Question 12

Determine the null space of

Accepted Answer

The answer of Determine the null space of
  ...

Question 13

If 
   
, 
   
, and 
   are subspaces of Rn, then their intersection 
   is also a subspace of Rn.

Accepted Answer

A) True 
 B)False

Question 14

By forming matrix rows, find a basis for the given subspace S and give the dimension of S, where

Accepted Answer

Basis: 
 @#IMG-DLM&

Question 15

If B is a basis for a given subspace, and u and v are vectors in span (B) such that 
   
, then 
   
.

Accepted Answer

A) True 
 B)False

Question 16

Find the change of basis matrix from the standard basis to B, and then convert x to the coordinate vector with respect to B.

Accepted Answer

The answer of Find the change of basis matrix from...

Question 17

The null space of an 
   matrix A is a subspace of Rn if and only if A is invertible.

Accepted Answer

A) True 
 B)False

Question 18

Convert the coordinate vector 
   from the given basis B to the standard basis.

Accepted Answer

The answer of Convert the coordinate vector 
  ...

Question 19

Find 
   given 
   
, where

Accepted Answer

The answer of Find 
   given 
 ...

Question 20

Determine the null space of

Accepted Answer

The answer of Determine the null space of
  ...

Find all values of so that rank , where

If and , then is a matrix.

If B is a basis for a given subspace, and u is in span (B) with , then .

Find the change of basis matrix from B₁ to B₂.

Determine the null space of

If B is a basis, then for all scalars , and all vectors , in span (B).

Let A be an matrix, and B an matrix. Then the null space of B is a subspace of the null space of AB.

By forming matrix columns, find a basis for the given subspace S and give the dimension of S, where

Find a basis for the null space of the given matrix A and give .

Determine the null space of

Expand the given set to form a basis for R⁴.

Determine the null space of

If , , and are subspaces of Rⁿ, then their intersection is also a subspace of Rⁿ.

By forming matrix rows, find a basis for the given subspace S and give the dimension of S, where

If B is a basis for a given subspace, and u and v are vectors in span (B) such that , then .

Find the change of basis matrix from the standard basis to B, and then convert x to the coordinate vector with respect to B.

The null space of an matrix A is a subspace of Rⁿ if and only if A is invertible.

Convert the coordinate vector from the given basis B to the standard basis.

Find given , where

Determine the null space of

Systems of Linear Equations

Euclidean Space

Matrices

Determinants

Eigenvalues and Eigenvectors

Vector Spaces

Orthogonality

Linear Transformations

Inner Product Spaces

Additional Topics and Applications

Filters

Exam 4: Subspaces

Find all values of so that rank , where

If and , then is a matrix.

If B is a basis for a given subspace, and u is in span (B) with , then .

Find the change of basis matrix from B1 to B2.

Determine the null space of

If B is a basis, then for all scalars , and all vectors , in span (B).

Let A be an matrix, and B an matrix. Then the null space of B is a subspace of the null space of AB.

By forming matrix columns, find a basis for the given subspace S and give the dimension of S, where

Find a basis for the null space of the given matrix A and give .

Determine the null space of

Expand the given set to form a basis for R4.

Determine the null space of

If , , and are subspaces of Rn, then their intersection is also a subspace of Rn.

By forming matrix rows, find a basis for the given subspace S and give the dimension of S, where

If B is a basis for a given subspace, and u and v are vectors in span (B) such that , then .

Find the change of basis matrix from the standard basis to B, and then convert x to the coordinate vector with respect to B.

The null space of an matrix A is a subspace of Rn if and only if A is invertible.

Convert the coordinate vector from the given basis B to the standard basis.

Find given , where

Determine the null space of

Systems of Linear Equations

Euclidean Space

Matrices

Determinants

Eigenvalues and Eigenvectors

Vector Spaces

Orthogonality

Linear Transformations

Inner Product Spaces

Additional Topics and Applications

Filters

Find the change of basis matrix from B₁ to B₂.

Expand the given set to form a basis for R⁴.

If , , and are subspaces of Rⁿ, then their intersection is also a subspace of Rⁿ.

The null space of an matrix A is a subspace of Rⁿ if and only if A is invertible.