Question 1

The 
  identity matrix 
  is a regular stochastic matrix.

Accepted Answer

A) True 
 B)False  False

Question 2

Find 
  
, given that

Accepted Answer

The answer of Find 
  
, given that
 ...

Question 3

Use the given LU factorization to solve 
  where

Accepted Answer

The answer of Use the given LU factorization to solve...

Question 4

Every matrix 
  has an LU factorization.

Accepted Answer

A) True 
 B)False

Question 5

If 
  and 
  are 
  doubly stochastic matrices, then AB is a doubly stochastic matrix.

Accepted Answer

A) True 
 B)False

Question 6

If 
  is a one-to-one linear transformation from R2 to R2, then the image of the unit square under 
  is a parallelogram with positive area.

Accepted Answer

A) True 
 B)False

Question 7

If 
  is a square invertible matrix, then 
  is an invertible matrix for every positive integer 
  
, with

Accepted Answer

A) True 
 B)False

Question 8

A matrix 
  is doubly stochastic if and only if 
  is doubly stochastic.

Accepted Answer

A) True 
 B)False

Question 9

Find all steady-state vectors for the given stochastic matrix.

Accepted Answer

The answer of Find all steady-state vectors for the given...

Question 10

Determine whether 
  is one-to-one, and whether 
  is onto, where 
  and

Accepted Answer

The answer of Determine whether 
  is one-to-one, and...

Question 11

Find an LDU factorization of

Accepted Answer

The answer of Find an LDU factorization of
 ...

Question 12

Use an augmented matrix and row operations to find the inverse of

Accepted Answer

The answer of Use an augmented matrix and row operations...

Question 13

Use the matrix
  to find the solutions to the linear system

Accepted Answer

The answer of Use the matrix
  to find the...

Question 14

Evaluate AB-BA, where

Accepted Answer

The answer of Evaluate AB-BA, where
 ...

Question 15

Determine if the given vector is in the range of 
  where

Accepted Answer

The answer of Determine if the given vector is in...

Question 16

If 
  for a matrix 
  
, and 
  is an onto linear transformation, then the number of columns of 
  is greater than or equal to the number of rows of 
  
.

Accepted Answer

A) True 
 B)False

Question 17

Find an LU factorization of

Accepted Answer

The answer of Find an LU factorization of
 ...

Question 18

If 
  and 
  are 
  invertible matrices, then so is

Accepted Answer

A) True 
 B)False

Question 19

Find the state vector 
  for the given stochastic matrix and initial state vector.

Accepted Answer

The answer of Find the state vector 
  for...

Question 20

Solve for the scalars a, b, c in the following equation:

Accepted Answer

The answer of Solve for the scalars a, b, c...

Exam 3: Matrices

The identity matrix is a regular stochastic matrix.

Find , given that

Use the given LU factorization to solve where

Every matrix has an LU factorization.

If and are doubly stochastic matrices, then AB is a doubly stochastic matrix.

If is a one-to-one linear transformation from R² to R², then the image of the unit square under is a parallelogram with positive area.

If is a square invertible matrix, then is an invertible matrix for every positive integer , with

A matrix is doubly stochastic if and only if is doubly stochastic.

Find all steady-state vectors for the given stochastic matrix.

Determine whether is one-to-one, and whether is onto, where and

Find an LDU factorization of

Use an augmented matrix and row operations to find the inverse of

Use the matrix to find the solutions to the linear system

Evaluate AB-BA, where

Determine if the given vector is in the range of where

If for a matrix , and is an onto linear transformation, then the number of columns of is greater than or equal to the number of rows of .

Find an LU factorization of

If and are invertible matrices, then so is

Find the state vector for the given stochastic matrix and initial state vector.

Solve for the scalars a, b, c in the following equation:

Exam 3: Matrices

The identity matrix is a regular stochastic matrix.

Find , given that

Use the given LU factorization to solve where

Every matrix has an LU factorization.

If and are doubly stochastic matrices, then AB is a doubly stochastic matrix.

If is a one-to-one linear transformation from R2 to R2, then the image of the unit square under is a parallelogram with positive area.

If is a square invertible matrix, then is an invertible matrix for every positive integer , with

A matrix is doubly stochastic if and only if is doubly stochastic.

Find all steady-state vectors for the given stochastic matrix.

Determine whether is one-to-one, and whether is onto, where and

Find an LDU factorization of

Use an augmented matrix and row operations to find the inverse of

Use the matrix to find the solutions to the linear system

Evaluate AB-BA, where

Determine if the given vector is in the range of where

If for a matrix , and is an onto linear transformation, then the number of columns of is greater than or equal to the number of rows of .

Find an LU factorization of

If and are invertible matrices, then so is

Find the state vector for the given stochastic matrix and initial state vector.

Solve for the scalars a, b, c in the following equation:

If is a one-to-one linear transformation from R² to R², then the image of the unit square under is a parallelogram with positive area.