Basics

Matrix = representing data in a rectangular array.

Matrices (plural for matrix) are named by a capital letter.  

Rows and Columns

One way to represent data is in a matrix. An m×n matrix has m rows and n columns, and each entry is given a unique name, based on its row and column:

Rows are horizontal

Columns are vertical

Matrix Dimensions

The dimensions of a matrix are decided by the number of rows and columns, with the row number coming first.  In some cases writing the dimension of the matrix below its name is useful.

For example in the matrices below, matrix E has dimensions 4x2, matrix F is 5x1, and matrix G is 1x4.

Matrix Dimensions Practice: Find the dimensions of each matrix.

#1) A
#2) B

Entries

Each entry in a matrix has a specific address.  The letter "a" refers to the entry coming from A and the first number after the letter refers to the row number and the second letter refers to the column number.

So for example, a₃₄ = 28 refers to the entry in row 3 and column 4 from matrix A.

So for example, b21 = 4 refers to the entry in row 2 and column 1 from matrix B.

Entries Practice: Find the value of each entry.

#1)  a₄₁ =

#2)  a₂₁  =

#3)  b₃₂  =

#4)  b₁₂ =

Homework

Dimensions 

Name the dimensions of each matrix.

#1) A

#2) B

#3) C

#4) D

#5) E

#6) F

Entries

Using A and B, find the values of each entry.

#1)  a₁₁ =

#2)  b₁₁ =

#3)  a₂₁ =

#4)  a₃₁ =

#5)  b₁₂ =

#6)  b₁₃ =

#7)  b₂₄ =

#8)  a₃₂ =

#9)  a₃₄ =

Answers Dimensions

#1)  A_1x5 

#2)  B_2x5 

#3)  C_8x1 

#4)  D_4x3 

#5)  E_2x2 

#6)  F_3x6 

Answers Entries

#1)  a₁₁ = 52

#2)  b₁₁ = 1

#3)  a₂₁ = 78

#4)  a₃₁ = 20

#5)  b₁₂ = 2

#6)  b₁₃ = 7

#7)  b₂₄ = 9

#8)  a₃₂ = 22

#9)  a₃₄ = 26