Pure: Matrices

Question 1

What does the matrix representing a stretch parallel to the x-axis with scale factor k look like?
2x2

Answer 1

k 0

0 1

Question 2

What does the matrix representing a stretch parallel to the y-axis with scale factor k look like?
2x2

Answer 2

1 0

0 k

Question 3

What does the matrix representing an enlargement, centre the origin, with scale factor k look like?
2x2

Answer 3

k 0

0 k

Question 4

What does the matrix representing a rotation 90° anticlockwise about the origin look like?
2x2

Answer 4

0 -1

1 0

Question 5

What does the matrix representing a rotation 180° about the origin look like?
2x2

Answer 5

-1 0

0 -1

Question 6

What does the matrix representing a rotation 90° clockwise about the origin look like?
2x2

Answer 6

0 1

-1 0

Question 7

What does the matrix representing an anticlockwise rotation through any angle θ look like?
2x2

Answer 7

cosθ -sinθ

sinθ cosθ

Question 8

What does the matrix representing a reflection in the x-axis look like?
2x2

Answer 8

1 0

0 -1

Question 9

What does the matrix representing a reflection in the y-axis look like?
2x2

Answer 9

-1 0

0 1

Question 10

What does the matrix representing a reflection in the line y = x look like?
2x2

Answer 10

0 1

1 0

Question 11

What does the matrix representing a reflection in the line y = -x look like?
2x2

Answer 11

0 -1

-1 0

Question 12

What does the matrix representing a shear parallel to the x-axis with factor k look like?
2x2

Answer 12

1 k

0 1

Question 13

What does the matrix representing a shear parallel to the y-axis with factor k look like?
2x2

Answer 13

1 0

k 1

Question 14

What does the matrix representing a reflection in the plane x = 0 look like?
3x3

Answer 14

-1 0 0
0 1 0
0 0 1

Question 15

What does the matrix representing a reflection in the plane y = 0 look like?
3x3

Answer 15

1 0 0
0 -1 0
0 0 1

Question 16

What does the matrix representing a reflection in the plane z = 0 look like?
3x3

Answer 16

1 0 0
0 1 0
0 0 -1

Question 17

What does the matrix representing a reflection in the plane y = z look like?
3x3

Answer 17

1 0 0
0 0 1
0 1 0

Question 18

What does the matrix representing a reflection in the plane x = y look like?
3x3

Answer 18

0 1 0
1 0 0
0 0 1

Question 19

What does the matrix representing a reflection in the plane x = z look like?
3x3

Answer 19

0 0 1
0 1 0
1 0 0

Question 20

What does the matrix representing a rotation 90° about the x-axis look like?
3x3

Answer 20

1 0 0
0 0 -1
0 1 0

Question 21

What does the matrix representing a rotation 90° about the y-axis look like?
3x3

Answer 21

0 0 -1
0 1 0
1 0 0

Question 22

What does the matrix representing a rotation 90° about the z-axis look like?
3x3

Answer 22

0 -1 0
1 0 0
0 0 1

Question 23

What does the matrix representing a stretch by factor k in the x direction look like?
3x3

Answer 23

k 0 0
0 1 0
0 0 1

Question 24

What does the matrix representing a stretch by factor k in the x direction and y direction look like?
3x3

Answer 24

k 0 0
0 k 0
0 0 1

Question 25

What does the matrix representing a stretch by factor k in the z direction and y direction look like?
3x3

Answer 25

1 0 0
0 k 0
0 0 k