1. Reflection about the line y=0, the axis, is accomplished with the transformation matrix with how many elements as ‘0’?
a) 8
b) 9
c) 4
d) 6
Explanation: The matrix used for reflection about y=0 is an identity matrix with 6 ‘0’s and two ‘1’s and one element as ‘-1’.
2. Which transformation distorts the shape of an object such that the transformed shape appears as if the object were composed of internal layers that had been caused to slide over each other?
a) Rotation
b) Scaling up
c) Scaling down
d) Shearing
Explanation: Two common shearing transformations are the type of transformation that shift coordinate x values coordinate y values. In shear transformation, the transformed shape appears as if the object were composed of internal layers that had been caused to slide over each other.
3. Transpose of a column matrix is________________
a) Zero matrix
b) Identity matrix
c) Row matrix
d) Diagonal matrix
Explanation: Transpose of a matrix is a matrix which is made by interchanging the rows and columns of the original matrix. Hence the transpose of column matrix is row matrix and vice versa.
4. Reversing the order in which a sequence of transformations is performed may affect the transformed position of an object.
a) True
b) False
Explanation: As we know that, matrix transformations are not commutative and the order of transformation matters. So it will affect the position of the object.
5. Which one of the following is the correct notation of a matrix with ‘m’ rows and ’n’ columns?
a) m + n
b) m – n
c) m x n
d) m/n
Explanation: m x n represents a matrix with ‘m’ number of rows and ‘n’ number of columns, while others are just arithmetic operations which can be done on 2 matrices.
6. How many minimum numbers of zeros are there in ‘3 x 3’ triangular matrix?
a) 4
b) 3
c) 5
d) 6
Explanation: In a triangular matrix, all entries, either above or below the diagonal are zero. So in case of ‘3 x 3’ matrix, there should be minimum 3 elements as 0.
7. In a rotation, by how much angle is the object rotated?
a) 45 degree
b) 90 degree
c) 180 degree
d) 360 degree
Explanation: Reflection is the mirror image of the original object. It rotates the object 1890 degrees. The left side image is formed into right side and vice versa.
8. Reflection is a special case of rotation.
a) True
b) False
Explanation: Reflection is a special case of rotation of 180° about a line in xy plane passing through the origin.
9. If two pure reflections about a line passing through the origin are applied successively the result is ___________________
a) Pure rotation
b) Quarter rotation
c) Half rotation
d) True reflection
Explanation: When we apply reflection one time, it rotates the image by 180 degrees. So, if we repeat it 2 times the total reflection will be of 360 degrees.
10. What is the determinant of the pure reflection matrix?
a) 1
b) 0
c) -1
d) 2
Explanation: The pure reflection matrix is:
[T] = | 1 0 |
| 0 -1|
So, the determinant will be = (1) (-1) – (0) (0) = 0.