Pure 6: Matrices

Question 1

What is a square matrix?

Answer 1

A matrix where there is the same number of rows and columns

Question 2

What is a zero matrix? (2)

Answer 2

A matrix where every element is zero

The matrix is denoted by 0

Question 3

What is an identity matrix?

Answer 3

A square matrix in which the numbers in the leading diagonal (top left to bottom right) are 1 and the other elements are zero

Question 4

How are identity matrices denoted?

Answer 4

Ik where k (sub-script) is equal to the dimensions of the matrix

Question 5

How are matrices added and subtracted?

Answer 5

Add or subtract the corresponding elements in the two matrices

Question 6

What does additively conformable mean?

Answer 6

Two matrices that are the same size (meaning they can be added or subtracted)

Question 7

How do you multiply a matrix by a scalar?

Answer 7

Multiply all of the elements by the scalar

Question 8

How are matrices multiplied together?

Answer 8

Multiply the elements in each row of the left hand matrix by the corresponding elements in each column of the right hand matrix and add the results

Question 9

What does multiplicatively conformable mean?

Answer 9

The number of columns in the first matrix equals the number of rows in the second matrix

Question 10

What is the determinant of a 2x2 matrix?

Answer 10

ad - bc

Question 11

What is a singular matrix? (2)

Answer 11

A matrix with a determinant of zero

It has no inverse

Question 12

What is a non-singular matrix? (2)

Answer 12

A matrix with a determinant that is not zero

It has an inverse

Question 13

What is the determinant of a 3x3 matrix?

Answer 13

a(minor of a) - b(minor of b) + c(minor of c)

Question 14

What is the minor of an element from a 3x3 matrix?

Answer 14

The determinant of the 2x2 matrix that is formed when the row and column containing that element have been crossed out

Question 15

What is the inverse of a matrix?

Answer 15

The inverse of a matrix M is M^-1 where MM^-1 = M^(-1)M = I

Question 16

How is the inverse of a matrix found?

Answer 16

M^-1 = 1/detM x (d -b | -c a)

Question 17

If A and B are non-singular matrices then…?

Answer 17

(AB)^-1 = B^(-1)A^(-1)

Question 18

What is the transpose of a matrix?

Answer 18

A matrix where the rows and columns from the original are interchanged

Question 19

How do you find the inverse of a 3x3 matrix? (5)

Answer 19

Find detA
Form the matrix of minors, M
From M, form the matrix of cofactors, C
Write down the transpose of C, C^T
A^-1 = 1/detA C^T

Question 20

What is the matrix of minors?

Answer 20

Replace each of the elements with their minors

Question 21

What is the matrix of cofactors?

Answer 21

Change the signs of the elements b, d, f and h

Top middle, middle left, middle right, bottom middle