Matrices

Question 1

How do you multiply matrices with a whole number?

Answer 1

You multipy every number in the matrix by that.

Question 2

How do you add or subtract two matrices together?

Answer 2

You add and subtract the numbers that are in the same positions as one another.

Question 3

What is the transpose (a’) of a matrix?

Answer 3

Swap the rows and columbs.

Question 4

How do you multipy matrices?

Answer 4

You multiply the first number in the first row with the first number in the first coloum and add them, then the second number in the second row with the second number in the second row and add them and so on…

Question 5

What tells you the order of the matrix? and how can you tell if a matrix can be multiplied together?

Answer 5

The numbers on the outside of each matrix, eg 2x3 and 2x2 would be 2x3. If the two inner numbers dont match, they cannot be multiplied.

Question 6

What does  do?

Answer 6

It doesn’t do anything, if you multiply by it the matrix will be unchanged. A = A

Question 7

What is the formula of the determinant of a 2x2 matrix?

Answer 7

det A = ad - bc

Question 8

What is the formula of the determinant of a 3x3 matrix?

Answer 8

Look in the formlula sheet, it’s the same as the vector product.

Question 9

What is a singular matrix?

Answer 9

A matrix with a determinant of zero.

Question 10

What is the formula for the inverse of a 2x2 matrix?

Answer 10

(1 /det A) x (original matrix with a and d swapped and b and c’s signs changed)

Question 11

How to do the index of a 3x3 matrix?

Answer 11

form the augmented matrix by just have a diaganol line of 1s from top left to bottom right, with the rest zeros and multiply with the original matrix. Just like guassian elimination get zeros on the bottom left, then on the middle right and then on the top middle and right. You can divide rows by a number to get them equal to 1. You go the subtraction on BOTH sides.

Question 12

What is the formula for a matrix reflected in the x axis?
What is the formula for a matrix reflected in the y axis?
What is the formula for a matrix reflected in the line y = x?

Answer 12

Bottom right changes sign.
Top left changes sign
The numbers swap with the thing next to it

Question 13

How do you answer a matrix corresponding to a rotation of θ° anticlockwise about the origin question?

Answer 13

Just sub in value to equation in formula sheet and simplyfy. If asked to find a new point just make a vector with the coordinates and multiply it by the vector you just made.

Question 14

What is the formula for a scale factor matrix?

Answer 14

just multiply everything by the number.