Worksheet: Introduction to Matrices

In this worksheet, we will practice identifying matrices and determining the order of a matrix and the position of each of its elements.

Q1:

Which of the following is the matrix 𝐴 =  𝑎    , where 𝑖 = 1 and 𝑗 = 1 , 2 ?

  • A [ 𝑎 𝑎 ]    
  • B  𝑎 𝑎     
  • C  𝑎 𝑎     
  • D [ 𝑎 𝑎 ]    

Q2:

Find the matrix 𝐴 =  𝑎    , with an order of 3 × 3 , whose elements are given by the formula 𝑎 = 5 𝑥 + 4 𝑦   .

  • A  9 1 4 1 9 1 4 1 8 2 2 1 9 2 3 2 7 
  • B  9 1 3 1 7 1 4 1 8 2 2 1 7 2 2 2 7 
  • C  9 1 4 1 9 1 3 1 8 2 3 1 7 2 2 2 7 
  • D  9 1 3 1 7 1 4 1 8 2 2 1 9 2 3 2 7 

Q3:

Given that 𝐴 =  𝑎    where 𝑎 = 3 𝑖 + 5 𝑗 + 9   , find the matrix 𝐴  . That 𝐴 is 2 × 3 matrix.

  • A  1 7 2 0 2 3 2 2 2 5 2 8 
  • B  2 2 2 5 2 8 1 7 2 0 2 3 
  • C  1 7 2 2 2 0 2 5 2 3 2 8 
  • D  2 3 2 0 1 7 2 8 2 5 2 3 

Q4:

Which of the following is the matrix 𝐴 =  𝑎    , where 𝑖 = 1 , 2 and 𝑗 = 1 , 2 , 3 ?

  • A  𝑎 𝑎 𝑎 𝑎 𝑎 𝑎             
  • B  𝑎 𝑎 𝑎 𝑎 𝑎 𝑎             
  • C  𝑎 𝑎 𝑎 𝑎 𝑎 𝑎             
  • D  𝑎 𝑎 𝑎 𝑎 𝑎 𝑎             

Q5:

Given that 𝐴 is a matrix of order 3 × 2 , where 𝑎 = 0   , 𝑎 = 𝑎 − 3     , 𝑎 = 4   , 𝑎 = 1 2 𝑎     , 𝑎 = 8   , and 𝑎 = 1 4 𝑎     , determine 𝐴 .

  • A  0 5 4 0 8 0 
  • B  0 5 4 0 8 1 
  • C  5 0 0 4 1 8 
  • D  0 8 4 0 8 0 

Q6:

Given that 𝐴 =  − 2 4 − 7 − 1 9 9  𝐵 =  − 7 3 2 − 6 − 4 − 8 7 3 0  𝐶 =  2 − 5 − 4  , , , find 𝑎   , 𝑏   , and 𝑐   .

  • A 𝑎 = − 8   , 𝑏 = 4   , 𝑐 = − 5  
  • B 𝑎 = 4   , 𝑏 = − 6   , 𝑐 = − 5  
  • C 𝑎 = 9   , 𝑏 = − 6   , 𝑐 = − 5  
  • D 𝑎 = 9   , 𝑏 = 3   , 𝑐 = − 5  

Q7:

Given 𝐴 =  8 − 3 1 1 4 5 − 5 9 2 − 1 3 4 0 − 7  , what is 𝐴   ?

Q8:

Consider the matrices 𝐴 =  − 2 1 0 7 1 9 0  , 𝐵 = 𝐴  . Determine 𝑎   and 𝑏   .

  • A 𝑎 = 1 0   , 𝑏 = 1 0  
  • B 𝑎 = 1 0   , 𝑏 = − 2  
  • C 𝑎 = 9   , 𝑏 = 1  
  • D 𝑎 = − 2   , 𝑏 = − 2  
  • E 𝑎 = − 2   , 𝑏 = 1 0  

Q9:

Given 𝐴 =  8 − 3 1 1 4 5 − 5 9 2 − 1 3 4 0 − 7  , which are the negative entries of 𝐴 ?

  • A 𝐴    , 𝐴    , 𝐴    , 𝐴   
  • B 𝐴    , 𝐴    , 𝐴    , 𝐴   
  • C 𝐴    , 𝐴    , 𝐴    , 𝐴   
  • D 𝐴    , 𝐴    , 𝐴    , 𝐴   
  • E 𝐴    , 𝐴    , 𝐴    , 𝐴   

Q10:

Given that 𝐴 is a matrix of order 2 × 2 , with 𝑎 = 7   , 𝑎 = − 1 0   , 𝑎 = − 9   , and 𝑎 = 2   , find the matrix 𝐴 .

  • A [ 7 − 1 0 − 9 2 ]
  • B  7 − 9 − 1 0 2 
  • C ⎡ ⎢ ⎢ ⎣ 7 − 1 0 − 9 2 ⎤ ⎥ ⎥ ⎦
  • D  7 − 1 0 − 9 2 
  • E  7 − 1 0 2 − 9 

Q11:

The table below represents the prices of some drinks in a café. The café owner changes the prices of the drinks, so that each drink is now two times its original price. Determine the matrix that represents the new prices of the drinks.

Drink Small Size Big Size
Strawberry Juice 1.5 5.5
Orange Juice 2 8.5
Mango Juice 3.5 9
  • A  3 1 1 4 1 7 7 1 8 
  • B  1 . 5 5 . 5 2 8 . 5 3 . 5 9 
  • C  4 . 5 1 6 . 5 6 2 5 . 5 1 0 . 5 2 7 
  • D  3 . 5 7 . 5 4 1 0 . 5 5 . 5 1 1 

Q12:

The given bar chart shows actual and predicted data for several continents about the percent of the population who live in urban areas. Represent this data in a matrix where the rows represent years in order from past to future, and the columns represent the continents in alphabetical order.

  • A  0 . 1 5 0 . 1 7 0 . 5 1 0 . 4 2 0 . 6 4 0 . 3 7 0 . 4 1 0 . 7 2 0 . 7 6 0 . 7 9 0 . 5 1 0 . 5 4 0 . 7 8 0 . 8 4 0 . 8 7 
  • B  0 . 2 9 0 . 4 9 0 . 6 0 0 . 1 5 0 . 3 7 0 . 5 1 0 . 1 7 0 . 4 1 0 . 5 4 0 . 5 1 0 . 7 2 0 . 7 8 0 . 4 2 0 . 7 6 0 . 8 4 0 . 6 4 0 . 7 9 0 . 8 7 
  • C  4 9 6 0 1 5 3 7 5 1 4 1 5 4 5 1 7 2 7 8 7 6 8 4 6 4 7 9 8 7 
  • D  1 . 5 5 . 1 1 . 7 4 . 2 6 . 4 3 . 7 7 . 2 4 . 1 7 . 6 7 . 9 5 . 1 7 . 8 5 . 4 8 . 4 8 . 7 
  • E ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ 0 . 1 5 0 . 3 7 0 . 5 1 0 . 1 7 0 . 4 1 0 . 5 4 0 . 5 1 0 . 7 2 0 . 7 8 0 . 4 2 0 . 7 6 0 . 8 4 0 . 6 4 0 . 7 9 0 . 8 7 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

Q13:

The coach of a school basketball team recorded the statistics of three players in a tournament as follows: Daniel: 7 games, 15 shots, and 5 goals; James: 13 games, 24 shots, and 8 goals; and, Ethan: 16 games, 23 shots, and 19 goals. Order these data in a matrix where the rows represent the players from least goals to most, the first column gives the number of games, the second column gives the number of shots, and the third column gives the number of goals.

  • A  7 1 5 5 1 6 2 3 1 9 1 3 2 4 8 
  • B  7 1 5 5 1 3 2 3 8 1 6 2 4 1 9 
  • C  7 1 5 5 1 3 2 4 8 1 6 2 3 1 9 
  • D  1 6 2 3 1 9 1 3 2 4 8 7 1 5 5 

Q14:

A company produces televisions with 32-inch, 42-inch, and 48-inch screens. The first table gives the number of televisions of each screen size produced in factories A and B during January 2016. The second table gives the same information for February 2016. Express the total number of televisions of each screen size produced in the two months by each factory, A and B, in a matrix.

Screens produced during January 2016:

Factory 32 inches 42 inches 48 inches
A 820 770 500
B 690 660 620

Screens produced during February 2016:

Factory 32 inches 42 inches 48 inches
A 560 550 830
B 520 700 660
  • A  1 , 2 5 0 1 , 2 1 0 1 , 4 5 0 1 , 3 4 0 1 , 4 7 0 1 , 1 6 0 
  • B  1 , 3 8 0 1 , 3 6 0 1 , 3 3 0 1 , 2 1 0 1 , 2 1 0 1 , 2 8 0 
  • C  1 , 3 4 0 1 , 4 7 0 1 , 1 6 0 1 , 2 5 0 1 , 2 1 0 1 , 4 5 0 
  • D  1 , 3 8 0 1 , 3 2 0 1 , 3 3 0 1 , 2 1 0 1 , 3 6 0 1 , 2 8 0 

Q15:

The bar chart shows the number of kilowatt-hours of energy produced and consumed in three countries over a certain time period. Represent these data in a matrix whose rows represent Brazil, France, and Canada, in that order, and whose columns represent production and consumption, in that order.

  • A | | | | 6 0 9 0 4 5 7 5 8 5 7 0 | | | |
  • B  6 0 9 0 4 5 7 5 8 5 7 0 
  • C ⎧ ⎨ ⎩ 6 0 9 0 4 5 7 5 8 5 7 0 ⎫ ⎬ ⎭
  • D 6 0 9 0 4 5 7 5 8 5 7 0

Q16:

If the order of matrix 𝐴 is 3 × 2 , then how many 𝑟 𝑜 𝑤 𝑠 does it have?

Q17:

Find the order of the matrix 𝐴 = [ − 9 6 − 3 ] .

  • A 2 × 1
  • B 1 × 1
  • C 3 × 1
  • D 1 × 3
  • E 3 × 3

Q18:

How many elements are there in a matrix of order 9 × 7 ?

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