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Maple Ho’s

Math 1B Maple Lab Test

Question 1: Score 1/1

Before attempting this question you should work through the self-directed learning Module

"Lesson 10 - Further Linear Algebra" on UNSW Blackboard.

----------------------------------------------------------------------------------------------------------------

Use Maple to find the eigenvalues of

.

Enter the eigenvalues in the box below as a Maple set. (Eg, if the eigenvalues were 1, 2, 3, 4,

you should enter {1,2,3,4} .)

To avoid typing errors, you may copy and paste the following sequence of entries of :

-59469, 60056, -11468, 43500, 6019, -29005, 23370, -14188, 36462, 7277, 13340, -13070, -

20632, -3014, -650, -13520, 47960, -4176, 8308, 11420, -9269, -2296, -1260, -820, -28757

and edit it appropriately to create a matrix.

Solution:

A:=<<-59469, 60056, -11468, 43500, 6019>|< -29005, 23370, -14188, 36462, 7277>|<

13340, -13070, -20632, -3014, -650>|< -13520, 47960, -4176, 8308, 11420>|< -9269, -

2296, -1260, -820, -28757>>;

with(LinearAlgebra):

Eigenvalues(A);

Answer:

(Do not copy from Maple, take note of formatting, order of eigenvalues does not matter)

{-38590, -30872, -23154, -15436, 30872}

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Question 2: Score 1/1

Before attempting this question you should work through the self-directed learning Module

"Lesson 10 - Further Linear Algebra" on UNSW Blackboard.

----------------------------------------------------------------------------------------------------------------

Use Maple to find the rank of

.

To avoid typing errors, you can copy and paste the following sequence of entries of :

11572, -17744, 8104, -7108, 26860, 11287, 27466, -25076, 29447, -26435, -41749, -36022,

38372, -18029, 28985, -18340, -9400, 25520, -12980, 22100, 44806, 33148, -26288, 30686, -

15470

and edit it appropriately to make a matrix. Enter the rank of in the box below.

Solution:

A:=<<11572, -17744, 8104, -7108, 26860>|< 11287, 27466, -25076, 29447, -26435>|<

-41749, -36022, 38372, -18029, 28985>|< -18340, -9400, 25520, -12980, 22100>|<

44806, 33148, -26288, 30686, -15470>>;

with(LinearAlgebra):

Rank(A);

Answer:

5

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Question 14: Score 1/1

Which of the following is a correct Maple command that will define the line L, for use with

the geom3d package, to be the line passing through the point A and in the direction of the

vector ? You may assume that the geom3d package has already been loaded and the

point A has already been defined.

Answer:

line(L, [A, [1,2,3]])

Question 15: Score 1/1

Which of the following is a correct Maple command that will define the plane P, for use with

the geom3d package, to be the plane passing through the three points A, B and C? You may

assume that the geom3d package has already been loaded and the points A, B and C have

already been defined.

Answer:

plane(P, [A, B, C])

Question 16: Score 1/1

Which of the following is a correct Maple command that will define the plane P, for use with

the geom3d package, to be the line passing through the point A with normal vector

? You may assume that the geom3d package has already been loaded and the point A has

already been defined.

Answer:

plane(P, [A, [1,2,3]])

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Question 17: Score 1/1

Which of the following is a correct Maple command that will define the sphere S, for use

with the geom3d package, to be the sphere with centre A and radius r? You may assume

that the geom3d package has already been loaded and the point A and radius r have

already been defined.

Answer:

sphere(S, [A, r])

Question 18: Score 1/1

Which of the following is a correct Maple command that will define the sphere S, for use

with the geom3d package, to be the sphere with a diameter being the line segment joining the

two points A and B? You may assume that the geom3d package has already been loaded and

the points A and B have already been defined.

Answer:

sphere(S, [A, B])

Question 19: Score 1/1

Which of the following is a correct Maple command that will define the sphere S, for use

with the geom3d package, to be the sphere passing through the four points A, B, C and

E? You may assume that the geom3d package has already been loaded and the points A, B,

C and E have already been defined.

(Note that the 4th point is called E to avoid using D which is used by Maple for

differentiating functions.)

Answer:

sphere(S, [A, B, C, E])

Question 20: Score 1/1

Which of the following is a correct Maple command from the geom3d package that will

define T to be the intersection of the two spheres S1 and S2? You may assume that the

geom3d package has already been loaded and the spheres S1 and S2 have already been

defined.

(Note that although the help page for "geom3d,intersection" in Maple does not include the

case of two spheres, "intersection" works for two spheres using a form similar to the

intersection of two planes.)

Answer:

intersection(T, S1, S2)

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Question 27: Score 3/3

A simple iteration procedure with and

, ,

is being used to find an approximate solution to the equation .

Select the correct expressions from the drop down menus to define a procedure which takes a

positive integer m and uses a for loop to calculate . The procedure should

return if and otherwise. All calculations are done using

30 significant figures.

Answer: (Green highlight = multiple choice)

Digits := 30; # shift + enter

f := proc(m) # shift + enter

local a,i; # shift + enter

a[0] := 0; # shift + enter

for i from 1 to m do # shift + enter

a[i] := evalf(sin((1+a[i-1]/6)^2)) # shift + enter

end do; # shift + enter

if abs(a[m]-a[m-1]) <10^(-16) then # shift + enter

a[m] # shift + enter

else # shift + enter

-1 # shift + enter

end if # shift + enter

end proc;

Use this procedure to calculate and and enter your answers in the box below as

decimal approximations correct to 30 significant figures. To prevent typing errors, you can

copy and paste your answers from your Maple worksheet.

The value of is

Solution:

f(9);

Answer:

-1

The value of is

Solution:

f(20);

Answer:

0.976125175779941224727247391125

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Good Luck!

1

Maple Ho’s

Math 1B Maple Lab Test

Question 1: Score 1/1

Before attempting this question you should work through the self-directed learning Module

"Lesson 10 - Further Linear Algebra" on UNSW Blackboard.

----------------------------------------------------------------------------------------------------------------

Use Maple to find the eigenvalues of

.

Enter the eigenvalues in the box below as a Maple set. (Eg, if the eigenvalues were 1, 2, 3, 4,

you should enter {1,2,3,4} .)

To avoid typing errors, you may copy and paste the following sequence of entries of :

-59469, 60056, -11468, 43500, 6019, -29005, 23370, -14188, 36462, 7277, 13340, -13070, -

20632, -3014, -650, -13520, 47960, -4176, 8308, 11420, -9269, -2296, -1260, -820, -28757

and edit it appropriately to create a matrix.

Solution:

A:=<<-59469, 60056, -11468, 43500, 6019>|< -29005, 23370, -14188, 36462, 7277>|<

13340, -13070, -20632, -3014, -650>|< -13520, 47960, -4176, 8308, 11420>|< -9269, -

2296, -1260, -820, -28757>>;

with(LinearAlgebra):

Eigenvalues(A);

Answer:

(Do not copy from Maple, take note of formatting, order of eigenvalues does not matter)

{-38590, -30872, -23154, -15436, 30872}

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2

Question 2: Score 1/1

Before attempting this question you should work through the self-directed learning Module

"Lesson 10 - Further Linear Algebra" on UNSW Blackboard.

----------------------------------------------------------------------------------------------------------------

Use Maple to find the rank of

.

To avoid typing errors, you can copy and paste the following sequence of entries of :

11572, -17744, 8104, -7108, 26860, 11287, 27466, -25076, 29447, -26435, -41749, -36022,

38372, -18029, 28985, -18340, -9400, 25520, -12980, 22100, 44806, 33148, -26288, 30686, -

15470

and edit it appropriately to make a matrix. Enter the rank of in the box below.

Solution:

A:=<<11572, -17744, 8104, -7108, 26860>|< 11287, 27466, -25076, 29447, -26435>|<

-41749, -36022, 38372, -18029, 28985>|< -18340, -9400, 25520, -12980, 22100>|<

44806, 33148, -26288, 30686, -15470>>;

with(LinearAlgebra):

Rank(A);

Answer:

5

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Question 14: Score 1/1

Which of the following is a correct Maple command that will define the line L, for use with

the geom3d package, to be the line passing through the point A and in the direction of the

vector ? You may assume that the geom3d package has already been loaded and the

point A has already been defined.

Answer:

line(L, [A, [1,2,3]])

Question 15: Score 1/1

Which of the following is a correct Maple command that will define the plane P, for use with

the geom3d package, to be the plane passing through the three points A, B and C? You may

assume that the geom3d package has already been loaded and the points A, B and C have

already been defined.

Answer:

plane(P, [A, B, C])

Question 16: Score 1/1

Which of the following is a correct Maple command that will define the plane P, for use with

the geom3d package, to be the line passing through the point A with normal vector

? You may assume that the geom3d package has already been loaded and the point A has

already been defined.

Answer:

plane(P, [A, [1,2,3]])

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Question 17: Score 1/1

Which of the following is a correct Maple command that will define the sphere S, for use

with the geom3d package, to be the sphere with centre A and radius r? You may assume

that the geom3d package has already been loaded and the point A and radius r have

already been defined.

Answer:

sphere(S, [A, r])

Question 18: Score 1/1

Which of the following is a correct Maple command that will define the sphere S, for use

with the geom3d package, to be the sphere with a diameter being the line segment joining the

two points A and B? You may assume that the geom3d package has already been loaded and

the points A and B have already been defined.

Answer:

sphere(S, [A, B])

Question 19: Score 1/1

Which of the following is a correct Maple command that will define the sphere S, for use

with the geom3d package, to be the sphere passing through the four points A, B, C and

E? You may assume that the geom3d package has already been loaded and the points A, B,

C and E have already been defined.

(Note that the 4th point is called E to avoid using D which is used by Maple for

differentiating functions.)

Answer:

sphere(S, [A, B, C, E])

Question 20: Score 1/1

Which of the following is a correct Maple command from the geom3d package that will

define T to be the intersection of the two spheres S1 and S2? You may assume that the

geom3d package has already been loaded and the spheres S1 and S2 have already been

defined.

(Note that although the help page for "geom3d,intersection" in Maple does not include the

case of two spheres, "intersection" works for two spheres using a form similar to the

intersection of two planes.)

Answer:

intersection(T, S1, S2)

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Question 27: Score 3/3

A simple iteration procedure with and

, ,

is being used to find an approximate solution to the equation .

Select the correct expressions from the drop down menus to define a procedure which takes a

positive integer m and uses a for loop to calculate . The procedure should

return if and otherwise. All calculations are done using

30 significant figures.

Answer: (Green highlight = multiple choice)

Digits := 30; # shift + enter

f := proc(m) # shift + enter

local a,i; # shift + enter

a[0] := 0; # shift + enter

for i from 1 to m do # shift + enter

a[i] := evalf(sin((1+a[i-1]/6)^2)) # shift + enter

end do; # shift + enter

if abs(a[m]-a[m-1]) <10^(-16) then # shift + enter

a[m] # shift + enter

else # shift + enter

-1 # shift + enter

end if # shift + enter

end proc;

Use this procedure to calculate and and enter your answers in the box below as

decimal approximations correct to 30 significant figures. To prevent typing errors, you can

copy and paste your answers from your Maple worksheet.

The value of is

Solution:

f(9);

Answer:

-1

The value of is

Solution:

f(20);

Answer:

0.976125175779941224727247391125

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18

Good Luck!