¡Descarga WEB 1- Algebra vectorial y más Ejercicios en PDF de Álgebra solo en Docsity!
Instituto
Polite´cnico Nacional Unidad Profesional Interdisciplinaria de Ingenier´ıa Campus Guanajuato
(ALU) -
16B AV BF Tarea1erDep. Fecha de Entrega: 02/26/2017 at 10:59am
CST.
A
lgebra Vectorial
1. (1 pt)
Let a = (-2, -3, -7) and b = (-2, 6, -10) be vectors. Compute
the following vectors.
A. a + b = ( , , )
B. 7 a = ( , , )
C. a - b = ( , , )
D. a =
Answer(s) submitted:
(incorrect)
Correct Answers:
2. (1 pt) Let u = 0 , 3 , v = 1 , 4 , and w = 2 , 5. Find
the vector x that satisfies
6 u − v + x = 10 x + w.
In this case, x =.
Answer(s) submitted:
(correct)
Correct Answers:
- <0.111111,3> 3. (1 pt) Find two vectors v 1 and v 2 whose sum is 4 , 1
, where v 1 is parallel to 4 , 5 while v 2 is perpendicular to 4 , 5.
v 1 = and
v 2
Answer(s) submitted:
(incorrect)
Correct Answers:
- <-1.07317,-1.34146>
- <-2.92683,2.34146> 4. (1 pt) Find a vector u that is parallel to the yz -plane and
perpendicular to the vector v = 0 , 4 , 2.
u =.
Hint: Hint: Can you find a second vector that must be per-
pendicular to u?
Answer(s) submitted:
(incorrect)
Correct Answers:
- <0,-2,4> 5. (1 pt) Find unit vectors that satisfy the given conditions:
(1) The unit vector in the same direction as 5 , 2 is
(2) The unit vector oppositely directed to 3 j k is
(3) The unit vector that has the same direction as the vec-
tor from the point A = ( 5 , 0 ) to the point B = ( 9 , 2 )
is
Answer(s) submitted:
(incorrect)
Correct Answers:
- <0.928477,0.371391>
- <0,-0.948683,0.316228>
- <0.894427,-0.447214> 6. (1 pt) In each part, find the two unit vectors in R
2
that
satisfy the given conditions.
(1) The two unit vectors parallel to the line y = 3 x 4 are
and.
(2) The two unit vectors parallel to the line 6 y x = 1 are
and.
(3) The two unit vectors perpendicular to the line y =
4 x are
and.
Answer(s) submitted:
5 t ) j +( 3 + 3 t ) k , rewrite this in terms of the symmetric
equations for the line.
(quotient involving x)
(quotient involving y) =
(quotient involving z) =
Answer(s) submitted:
(incorrect)
14. (1 pt) Consider the two
lines L 1 : x = 2 t, y = 1 + 2 t, z
= 3 t and
L
2 : x = 7 + 3 s, y = 4 + s, z = 1 + 5 s
Find the point of intersection of the two lines.
P = ( , , )
Answer(s) submitted:
(incorrect)
Correct Answers:
- 5
- 6 15. (1 pt) Determine whether the lines
Correct Answers:
5
and
L
1
x −
x +
y −
y +
z − 12
z +
L
2
13. (1 pt) Consider the line L ( t ) = 4 5 t, 18 + 4 t.
Then
L intersects:
(1) The x -axis at the point when t =.
(2) The y -axis at the point when t =.
(3) The parabola y = x
2
at the points and
when t = and.
Answer(s) submitted:
(incorrect)
Correct Answers:
- (18.5,0)
- -4.
- (0,14.8)
- -0.
- (-4.26782,18.2143)
- (3.46782,12.0257)
intersect, are skew, or are parallel. If they intersect,
determine the point of intersection; if not leave the
remaining answer blanks empty.
The lines
Point of intersection: ( , , )
Answer(s) submitted:
(incorrect)
Correct Answers:
16. (1 pt) Find the distance from the point (4, 1, 1) to the
line
x = 0 , y = 1 + 5 t, z = 1 + 4 t.
Answer(s) submitted:
(incorrect)
Correct Answers:
- Two planes parallel to a third plane are parallel.
- Two planes either intersect or are parallel.
- A plane and a line either intersect or are parallel.
- Two planes perpendicular to a third plane are parallel.
Answer(s) submitted:
(incorrect)
Correct Answers:
- F
- F
- F
- T
- T
- T
- F
- T
- T
- T
- F 24. (1 pt) What do the following equations represent in R
3
?
Match the two sets of letters:
a. a vertical plane
b. a horizontal plane
c. a plane which is neither vertical nor horizontal
A. − 6 x + 5 y = − 9
B. x = 1
25. (1 pt)
Find the point at which the line ⟨ 3 , − 1 , − 4 ⟩ + t ⟨− 4 , − 4 , − 1 ⟩
in- tersects the plane 2 x + 3 y + 5 z = −92.
Answer(s) submitted:
(incorrect)
Correct Answers:
26. (1 pt) (A) Find the parametric equations for the line
through the point P = (3, 0, -4) that is perpendicular to the
plane 5 x + 0 y 5 z = 1_._
Use ”t” as your variable, t = 0 should correspond to P, and the
velocity vector of the line should be the same as the standard
normal vector of the plane.
x =
y =
z =
(B) At what point Q does this line intersect the yz-
plane? Q = ( , , )
Answer(s) submitted:
(incorrect)
Correct Answers:
- 3 + t * 5
- 0 + t * 0
- -4 + t * -
- 0
C. y = 3
D. z = 1
Answer(s) submitted:
(incorrect)
Correct Answers:
- a
- a
- a
- b 27. (1 pt) Find an equation of the plane through the point (-
3, 3, -3) and parallel to the plane 5 x 2 y + 0 z = 4. Do this
problem in the standard way or WebWork may not recognize a
correct answer.
x + y + z =
Answer(s) submitted:
(incorrect)
Correct Answers:
A + B =
35. (1 pt) If A
and B =
Answer(s) submitted:
, then
(incorrect)
Correct Answers:
Answer(s) submitted:
(incorrect)
Correct Answers:
− 3 − 4 4
− 1 − 9
26 − 30
- False 38. (1 pt) Compute the following product.
3 − 3 3
− 2 − 1 − 8
36. (1 pt) If A =
and B =
Answer(s) submitted:
(incorrect)
Correct Answers:
4 A − 2 B =
and
39. (1 pt) Given the matrix A =
find A
3
T
A
3
=.
A =.
Answer(s) submitted:
(incorrect)
Correct Answers:
2 12 − 12
Answer(s) submitted:
(incorrect)
Correct Answers:
− 12 − 4 − 12
− 2 − 4 0
2 − 1 − 2
40. (1 pt) Evaluate the following matrix product.
1 − 2 − 3
− 1 − 2 2
37. (1 pt) If A
2 − 6 3 − 1
and B
, then
Answer(s) submitted:
AB = and
(incorrect) Correct Answers:
BA =.
? True or False: AB = BA for any two square matrices A
and B of the same size.
, then − 40 0
− 67 − 6
7 − 1
− 5 − 4
− 14 − − 47 − 76
Answer(s) submitted:
(incorrect)
Correct Answers:
0 − 36 − 15 − 4
0 0 − 35 − 1
0 0 0 − 24
×
47. (1 pt) If A, B, and C are 5 × 5 , 5 × 7 , and 7 × 6
matri-
50. (1 pt) Find the determinant of the matrix
A
(e.g. ”3 x 4”, with spaces between numbers and ”x”). For those
undefined, enter ”undefined”.
AC :
CB :
A
2
:
BA :
Answer(s) submitted:
det( A ) =.
Answer(s) submitted:
(incorrect)
Correct Answers:
- 52 51. (1 pt) Find the determinant of the matrix
• B = − 1 4 3
(incorrect)
Correct Answers:
- undefined
- undefined
- 5 x 5
- undefined 48. (1 pt)
If A and B are 6 5 matrices, and C is a 4 6 matrix, which of
the following are defined?
det( B ) =.
Answer(s) submitted:
(incorrect)
Correct Answers:
- 52 52. (1 pt) Find the determinant of the matrix
• A. A
T
C =
• B. B + A
• C. BA
T
• D. AB
• E. CA
• F. B + C
Answer(s) submitted:
(incorrect)
Correct Answers:
- ABDE 49. (1 pt) Solve for X.
+ 4 X =
det( C ) =.
Answer(s) submitted:
(incorrect)
Correct Answers:
k 0 0
(1 pt) If A = 0 1 0
then det( A ) =
Answer(s) submitted:
(incorrect)
Correct Answers:
X =
Answer(s) submitted:
(correct)
Correct Answers:
1 / 4 − 9 / 4
54. (1 pt) If A =
then det( A ) =
Answer(s) submitted:
ces respectively, determine which of the following products
are defined. For those defined, enter the size of the resulting
matrix
58. (1 pt) If A =
M =
a 7 5
55. (1 pt) If A
= then det( A ) =
Answer(s) submitted:
(incorrect)
Correct Answers:
60. (1 pt) If A =
then det( A ) =
Answer(s) submitted:
(incorrect)
Correct Answers:
det( M ) =.
Answer(s) submitted:
(incorrect)
Correct Answers:
- 8 57. (1 pt) Find the determinant of the matrix 61. (1 pt) Given the matrix A = a 1 8
6 9 a
find all values of a that make A = 0. Give your answer as a
comma-separated list.
Values of a :.
Answer(s) submitted:
A =
(incorrect)
Correct Answers:
- (-27+sqrt((27)ˆ2-4-8366))/(2-8), (-27-sqrt((27)ˆ2-4-
8*
62. (1 pt) If A and B are 2 × 2 matrices, det( A ) = 2,
det( A ) =.
Answer(s) submitted:
(incorrect)
Correct Answers:
then det( A ) =
Answer(s) submitted:
(incorrect)
Correct Answers:
det( B ) = 5, then
det( AB ) = ,
det( 2 A ) = ,
det( A
T
) = ,
det( B
− 1
) = ,
det( B
2
) =.
Answer(s) submitted:
(incorrect)
Correct Answers:
×
59. (1 pt) If A = 7 9 2 0 0
1 4 2 8 0
then det( A ) =
Answer(s) submitted:
(incorrect)
Correct Answers:
- 63. (1 pt) Find the determinant of the n n matrix A with
6’s on the diagonal, 1’s above the diagonal, and 0’s below the
diagonal.
det( A ) =.
Answer(s) submitted:
(incorrect)
Correct Answers:
×
× k ×
a b c
69. (1 pt) If det a b c
d e f
64. (1 pt) If det d e f
g h i
g h i
then det
a b c
g h i
d e f
then det
a b c
5 d + a 5 e + b 5 f
g h i
Answer(s) submitted:
(incorrect)
Correct Answers:
65. (1 pt) If the determinant of a 4 4 matrix A is det( A ) =
3, and the matrix C is obtained from A by swapping the first
and third columns, then det( C ) =.
Answer(s) submitted:
(incorrect)
Correct Answers:
a b c
Answer(s) submitted:
(incorrect)
Correct Answers:
- 10 70. (1 pt) If the determinant of a 4 4 matrix A is det( A ) =
4, and the matrix D is obtained from A by adding 7 times the
third row to the second, then det( D ) =.
Answer(s) submitted:
(incorrect)
Correct Answers:
66. (1 pt) If det d e
f
g h i
then det
a b c
2 d 2 e 2 f
g h i
71. (1 pt) The matrix
2 − 6
is invertible if and only if
Answer(s) submitted:
(incorrect)
Correct Answers:
67. (1 pt) If the
determinant of a 3 3 matrix A is det( A )
and the matrix B is obtained from A by
multiplying the first row
by 3, then det( B ) =.
Answer(s) submitted:
- 21 72. (1 pt) Given the matrix
(a) find its determinant;
Your answer is :
