Question 1

Sketch the graph of the cross product   of the unit vectors   ,   .

Accepted Answer

A)     
B)     
C)     
D)     
A)     
B)     
C)     
D)

Question 2

Find the least squares solution of the system   , where   .

Accepted Answer

A)    
B)    
C)    
D)    
E)     
A)    
B)    
C)    
D)    
E)

Question 3

​Verify the points   are the vertices of a parallelogram, then find its area.

Accepted Answer

The answer of ​Verify the points   are the...

Question 4

Determine all vectors v that are orthogonal to    .

Accepted Answer

A)    where t is any real numbers 
B)     where s and t are any real numbers 
C)    where s and t are any real numbers 
D)     where t is any real numbers 
E)    where s and t are any real numbers 
A)    where t is any real numbers 
B)     where s and t are any real numbers 
C)    where s and t are any real numbers 
D)     where t is any real numbers 
E)    where s and t are any real numbers

Question 5

Suppose that the following table shows the annual sales, in millions of dollars, for Advanced Auto Parts and Auto Zone for 2000 through 2007. Find the least squares quadratic model for Advanced Auto Parts. Let t represents the year, with   corresponding to 2000. Round all coefficients to two decimal places.

Accepted Answer

A)     
B)     
C)    
D)     
E)     
A)     
B)     
C)    
D)     
E)

Question 6

Find the area of the parallelogram that has the vectors   ,   as adjacent sides.

Accepted Answer

A)  9 
B)  27 
C)  729 
D)  18 
E)  6 
A)  9 
B)  27 
C)  729 
D)  18 
E)  6

Question 7

Determine all vectors v that are orthogonal to   .

Accepted Answer

A)    , where t is any real number 
B)    , where t is any real number 
C)     , where t is any real number 
D)    , where t is any real number 
E)     , where t is any real number 
A)    , where t is any real number 
B)    , where t is any real number 
C)     , where t is any real number 
D)    , where t is any real number 
E)     , where t is any real number

Question 8

Find the linear least squares approximating function g for the function   ,   .

Accepted Answer

A)     
B)     
C)     
D)    
E)    
A)     
B)     
C)     
D)    
E)

Question 9

Find   for the standard inner product defined in R3, where   .

Accepted Answer

A)      
B)      
C)       
D)       
E)       
A)      
B)      
C)       
D)       
E)

Question 10

Find the Fourier approximation of second order for the function   on the interval   .

Accepted Answer

A)    
B)    
C)     
D)     
E)     
A)    
B)    
C)     
D)     
E)

Question 11

Determine whether the set of vectors   in R3 is orthogonal (but not orthonormal), orthonormal, or neither.

Accepted Answer

A)  orthonormal 
B)  orthogonal 
C)  neither 
A)  orthonormal 
B)  orthogonal 
C)  neither

Question 12

Suppose that the table shows the world carbon dioxide emissions y in millions of metric tons during the years 1999 to 2004. Find the least squares regression line for the data. Let t represent the year, with   corresponding to 1999. Round your answer to four significant figures

Accepted Answer

A)     
B)     
C)    
D)    
E)     
A)     
B)     
C)    
D)    
E)

Question 13

Suppose that the following table shows the annual sales, in millions of dollars, for Advanced Auto Parts and Auto Zone for 2000 through 2007. Find the least squares quadratic model for Advanced Auto Parts and use the model to predict sales for the year 10. Let t represent the year, with   corresponding to 2000. Round all coefficients to two decimal places and the answer to nearest million dollars.

Accepted Answer

A)  $20,686 million 
B)  $34,086 million 
C)  $14,960 million 
D) $29,686 million 
E)  $10,448 million 
A)  $20,686 million 
B)  $34,086 million 
C)  $14,960 million 
D) $29,686 million 
E)  $10,448 million

Question 14

Use the Gram-Schmidt orthonormalization process to transform the basis   for R3 into an orthonormal basis. Use the Euclidean inner product for R3 and use the vectors in the order in which they are shown.

Accepted Answer

A)     
B)     
C)    
D)   
E)    
A)     
B)     
C)    
D)   
E)

Question 15

​Show that the cross product   of the vectors   ,   is orthogonal to both u and v.

Accepted Answer

The answer of ​Show that the cross product  ...

Question 16

Graph the points   and the least squares regression line for the data points on the same set of axes.

Accepted Answer

A)      
B)       
C)      
D)       
E)  none of the choices 
A)      
B)       
C)      
D)       
E)  none of the choices

Question 17

Find the triple scalar product   where   .

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 18

Find the cross product   of the unit vectors   .

Accepted Answer

A)     
B)     
C)     
D)    
E)     
A)     
B)     
C)     
D)    
E)

Question 19

Find the triple scalar product   where   ,   ,   .

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 20

Find   for the inner product   defined in R2, where   .

Accepted Answer

A)  8 
B)  48 
C)  6 
D)  58 
E)  43 
A)  8 
B)  48 
C)  6 
D)  58 
E)  43

Sketch the graph of the cross product of the unit vectors , .

Find the least squares solution of the system , where .

Verify the points are the vertices of a parallelogram, then find its area.

Determine all vectors v that are orthogonal to .

Find the area of the parallelogram that has the vectors , as adjacent sides.

Determine all vectors v that are orthogonal to .

Find the linear least squares approximating function g for the function , .

Find for the standard inner product defined in R³, where .

Find the Fourier approximation of second order for the function on the interval .

Determine whether the set of vectors in R³ is orthogonal (but not orthonormal), orthonormal, or neither.

Suppose that the table shows the world carbon dioxide emissions y in millions of metric tons during the years 1999 to 2004. Find the least squares regression line for the data. Let t represent the year, with corresponding to 1999. Round your answer to four significant figures

Use the Gram-Schmidt orthonormalization process to transform the basis for R³ into an orthonormal basis. Use the Euclidean inner product for R³ and use the vectors in the order in which they are shown.

Show that the cross product of the vectors , is orthogonal to both u and v.

Graph the points and the least squares regression line for the data points on the same set of axes.

Find the triple scalar product where .

Find the cross product of the unit vectors .

Find the triple scalar product where , , .

Find for the inner product defined in R², where .

Linear Equations

Matrices

Determinants

Vector Spaces

Linear Transformations

Eigenvalues Eigenvectors

Filters

Exam 5: Inner Product Spaces

Sketch the graph of the cross product of the unit vectors , .

Find the least squares solution of the system , where .

​Verify the points are the vertices of a parallelogram, then find its area.

Determine all vectors v that are orthogonal to .

Find the area of the parallelogram that has the vectors , as adjacent sides.

Determine all vectors v that are orthogonal to .

Find the linear least squares approximating function g for the function , .

Find for the standard inner product defined in R3, where .

Find the Fourier approximation of second order for the function on the interval .

Determine whether the set of vectors in R3 is orthogonal (but not orthonormal), orthonormal, or neither.

Suppose that the table shows the world carbon dioxide emissions y in millions of metric tons during the years 1999 to 2004. Find the least squares regression line for the data. Let t represent the year, with corresponding to 1999. Round your answer to four significant figures

Use the Gram-Schmidt orthonormalization process to transform the basis for R3 into an orthonormal basis. Use the Euclidean inner product for R3 and use the vectors in the order in which they are shown.

​Show that the cross product of the vectors , is orthogonal to both u and v.

Graph the points and the least squares regression line for the data points on the same set of axes.

Find the triple scalar product where .

Find the cross product of the unit vectors .

Find the triple scalar product where , , .

Find for the inner product defined in R2, where .

Linear Equations

Matrices

Determinants

Vector Spaces

Linear Transformations

Eigenvalues Eigenvectors

Filters

Verify the points are the vertices of a parallelogram, then find its area.

Find for the standard inner product defined in R³, where .

Determine whether the set of vectors in R³ is orthogonal (but not orthonormal), orthonormal, or neither.

Use the Gram-Schmidt orthonormalization process to transform the basis for R³ into an orthonormal basis. Use the Euclidean inner product for R³ and use the vectors in the order in which they are shown.

Show that the cross product of the vectors , is orthogonal to both u and v.

Find for the inner product defined in R², where .