QUESTION 10 Which of the following is a linear transformation? Translations Proj

Question

QUESTION 10 Which of the following is a linear transformation? Translations Projections Reflections Rotations scalings QUESTION 11 Which of the following is not true about affine transformations? They have the form) M+i They are a special type of linear transformation They can be represented using homogeneous representations OThey can be used to represent poses of robotic joints and virtual cameras QUESTION 12 A system of linear equations can be solved by Translating the equations into a matrix equation of the form Mx = b with unknown r Translating the equations into a matrix equation of the form Mi -bwith unknown b Representing the equations via a non-linear affine function and solving for the unknown linear component Translating the equations into a matrix equation of the form with unknown x and ?

Explanation / Answer

Answer 10:

b) Projections

d) Rotations

Explanation:

Most common geometric transformations that keep the origin fixed are linear. All linear transformations are built by combining simple geometric processes such as rotation, stretching, shrinking, shearing and projection.

Answer 11:

d) They can be used to represent poses of robotic joints and virtual cameras.

Answer 12:

a) Translating the equations into a matrix of the form Mx=b with unknown x

Explanation:

Let us consider following linear equations:

x + y + 3z = 6

2y + 5z = -4

2x + 5y - z = 27

We can write this as: Mx = b

where M is the 3*3 matrix of x, y and z coefficients

x is x, y and z

and b is 6, -4 and 27

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