Matricies

Question 1

When can two matrices be added together?

Answer 1

They can only be added of they are of exactly the same size

Question 2

What happens when multiplying a matrix by a single whole number?

Answer 2

Multiply each element by the whole number

Question 3

When can two matrices be multiplied together?

Answer 3

When the number of columns in the first matches the number of rows in the second.

Question 4

How do we multiply matricies?

Answer 4

Take all elements from top row of the first, multiply them by all the elements in first column of second and add together. This becomes the element in the top left of the matrix. Then take the same elements from the first, but the second column of the second. This becomes the second element on the top row of the new matrix. Repeat until all elements have been multiplied and added.

Question 5

How can translation be done with matricies?

Answer 5

An addition of two

Question 6

How can scaling be expressed with matricies?

Answer 6

Multiplication:

Sx 0 ) * (x) = (Sx x
(0 Sy) (y) (Sy y)

Question 7

How can rotation be done with matricies?

Answer 7

Multiplication:

cos(alpha) -sin(alpha) ) * (x) = (work it out
( sin(alpha) cos(alpha) ) (y)

Question 8

How can we make image manipulation more efficient?

Answer 8

If we want to rotate and scale at the same time, we should multiply the two matrices then the image matrix, rather than one after the other.