Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Multiplying Matrices

Sample Question Videos

Worksheet • 25 Questions • 5 Videos

Q1:

Given that find ( 𝐴 + 𝐡 ) 𝐴 .

  • A ο€Ό βˆ’ 1 1 1 βˆ’ 2 1 1 1 1 
  • B ο€Ό 5 9 βˆ’ 7 1 βˆ’ 4 9 6 1 
  • C ο€Ό βˆ’ 6 βˆ’ 4 βˆ’ 1 5 1 7 
  • D ο€Ό βˆ’ 1 βˆ’ 2 1 1 1 1 1 1 

Q2:

Given that find 𝐴 2 .

  • A ο€Ό 3 1 βˆ’ 1 5 2 0 
  • B ο€Ό 3 7 3 5 3 5 5 0 
  • C ο€Ό 3 1 5 βˆ’ 1 2 0 
  • D ο€Ό 6 1 βˆ’ 3 1 βˆ’ 3 1 2 6 

Q3:

Given that find 𝐴 𝐡 if possible.

  • A  0 3 5 0 βˆ’ 3 5 
  • B It is not possible.
  • C  0 0 3 5 βˆ’ 3 5 
  • D [ 0 βˆ’ 3 5 ]
  • E  0 βˆ’ 3 5 

Q4:

Given that 𝐴 = ο€Ό βˆ’ 5 βˆ’ 6 5 0  , find 𝐴 + 5 𝐴 + 3 0 𝐼 2 .

  • A ο€Ό 0 0 0 0 
  • B ο€Ό 1 0 0 1 
  • C ο€Ό 6 6 βˆ’ 5 5 0 5 5 
  • D ο€Ό 0 3 0 3 0 0 

Q5:

Determine the values of π‘₯ , 𝑦 , and 𝑧 that satisfy the following:

  • A π‘₯ = 1 , 𝑦 = 4 , 𝑧 = βˆ’ 9
  • B π‘₯ = βˆ’ 3 , 𝑦 = 2 0 , 𝑧 = βˆ’ 4
  • C π‘₯ = 1 , 𝑦 = 2 0 , 𝑧 = βˆ’ 1 4
  • D π‘₯ = βˆ’ 1 3 , 𝑦 = 8 , 𝑧 = βˆ’ 1 4

Q6:

Given that find 𝐴 𝐡 if possible.

  • A ο€Ό 7 5 
  • B it is not possible
  • C ( 7 5 )
  • D ο€Ό βˆ’ 1 8 2 8 βˆ’ 3 1 8 βˆ’ 1 6 3 
  • E  βˆ’ 1 8 1 8 2 8 βˆ’ 1 6 βˆ’ 3 3 

Q7:

Consider the matrices Find 𝐴 𝐡 , if possible.

  • A  βˆ’ 8 0 βˆ’ 1 1 5 4 8 1 6 6 8 1 2 βˆ’ 8 4 βˆ’ 7 1 0 5 
  • B  βˆ’ 8 0 1 6 βˆ’ 8 4 βˆ’ 1 1 5 6 8 βˆ’ 7 4 8 1 2 1 0 5 
  • C ο€Ό βˆ’ 8 8 3 6 4 2 8 3 2 6 3 
  • D  βˆ’ 8 8 8 3 6 3 2 4 2 6 3 

Q8:

Consider the matrices

Find if possible.

  • A
  • B
  • C
  • D

Q9:

Consider the matrices Find 𝐴 𝐢 𝐡 and 𝐡 𝐴 𝐢 if possible.

  • A 𝐴 𝐢 𝐡 =  0 0 βˆ’ 3 8 2 3  , 𝐡 𝐴 𝐢 =  5 3 3 0 1 8 
  • BIt is not possible.
  • C 𝐴 𝐢 𝐡 =  βˆ’ 3 0 3 0 βˆ’ 1 8 1 8  , 𝐡 𝐴 𝐢 =  5 3 0 3 1 8 
  • D 𝐴 𝐢 𝐡 =  0 βˆ’ 3 8 0 2 3  , 𝐡 𝐴 𝐢 =  βˆ’ 3 0 3 0 βˆ’ 1 8 1 8 
  • E 𝐴 𝐢 𝐡 =  βˆ’ 3 0 βˆ’ 1 8 3 0 1 8  , 𝐡 𝐴 𝐢 =  βˆ’ 3 0 βˆ’ 1 8 3 0 1 8 

Q10:

Consider the matrices

Find .

  • A
  • B
  • C
  • D
  • E

Find .

  • A
  • B
  • C
  • D
  • E

Q11:

Suppose

Find the product .

  • A
  • B
  • C
  • D
  • E

Find the product .

  • A
  • B
  • C
  • D
  • E

Q12:

Evaluate the matrix product

  • A
  • B
  • C
  • D
  • E

Q13:

Consider the matrix product

What can you conclude about it?

  • AFor a given 2 Γ— 3 matrix 𝐴 , there can be a matrix 𝐡 that is not the 2 Γ— 2 identity matrix for which 𝐡 𝐴 = 𝐴 .
  • BFor a given 2 Γ— 3 matrix 𝐴 , there can be a matrix 𝐡 that is not the 3 Γ— 3 identity matrix for which 𝐴 𝐡 = 𝐴 .
  • CFor a given 2 Γ— 3 matrix 𝐴 , there cannot be any matrix 𝐡 except the 2 Γ— 2 identity matrix for which 𝐡 𝐴 = 𝐴 .
  • D For a given 2 Γ— 3 matrix 𝐴 , there can be a matrix 𝐡 that is not the 3 Γ— 3 identity matrix for which 𝐴 𝐡 = 𝐡 .

Is it possible to find a matrix 𝐡 with the above property for every 2 Γ— 3 matrix 𝐴 ?

  • Ayes
  • Bno

Q14:

Consider the matrices

Find 𝐴 𝐡 𝑇 and 𝐴 𝐡 𝑇 .

  • A 𝐴 𝐡 = ο€Ό 1 4 4 βˆ’ 1 6 βˆ’ 2  𝑇 , 𝐴 𝐡 = ο€Ό 1 8 βˆ’ 4 3 6 βˆ’ 6  𝑇
  • B 𝐴 𝐡 = ο€Ό 1 4 βˆ’ 1 6 4 βˆ’ 2  𝑇 , 𝐴 𝐡 = ο€Ό 1 8 3 6 βˆ’ 4 βˆ’ 6  𝑇
  • C 𝐴 𝐡 = ο€Ό 1 4 4 βˆ’ 1 6 βˆ’ 2  𝑇 , 𝐴 𝐡 = ο€Ό 1 4 4 βˆ’ 1 6 βˆ’ 2  𝑇
  • D 𝐴 𝐡 = ο€Ό 2 6 βˆ’ 4 βˆ’ 4 2  𝑇 , 𝐴 𝐡 = ο€Ό 2 6 βˆ’ 4 βˆ’ 4 2  𝑇

Q15:

Let π‘₯ = ( βˆ’ 1 βˆ’ 1 1 ) and 𝑦 = ( 0 1 2 ) . Find π‘₯ 𝑦 𝑇 and π‘₯ 𝑦 𝑇 .

  • A  0 βˆ’ 1 βˆ’ 2 0 βˆ’ 1 βˆ’ 2 0 1 2  , 1
  • B  0 0 0 βˆ’ 1 βˆ’ 1 1 2 2 2  , 1
  • C  0 βˆ’ 1 βˆ’ 2 0 βˆ’ 1 βˆ’ 2 0 1 2  , βˆ’ 1
  • D  0 1 2 0 1 2 0 βˆ’ 1 βˆ’ 2  , βˆ’ 1
  • E  0 1 2 0 1 2 0 βˆ’ 1 βˆ’ 2  , 1

Q16:

Consider the matrices Find 𝐴 𝐡 𝐢 if possible.

  • A ο€Ό 3 βˆ’ 3 6 βˆ’ 9 9 0 
  • B ο€Ό 3 βˆ’ 9 βˆ’ 3 6 9 0 
  • C ο€Ό 2 7 βˆ’ 3 3 βˆ’ 3 6 4 2 
  • D ο€Ό 2 7 βˆ’ 3 6 βˆ’ 3 3 4 2 

Q17:

Given that and 𝐼 is the unit matrix of the same order, find the matrix 𝑋 for which 𝐴 𝐡 = 𝑋 Γ— 𝐼 .

Q18:

Given that find 𝐴 𝐡 if possible.

  • A ο€Ό 0 0 1 1 
  • B ο€Ό 1 1 0 0 
  • C ο€Ό 0 0 βˆ’ 1 βˆ’ 1 
  • D ο€Ό βˆ’ 1 βˆ’ 1 0 0 

Q19:

Given that and 𝑖 = βˆ’ 1 2 , find 𝐴 𝐡 if possible.

  • A ο€Ό βˆ’ 1 1 0 0 
  • B ο€Ό 1 βˆ’ 1 0 0 
  • C ο€Ό 2 0 0 0 
  • D ο€Ό βˆ’ 2 0 0 0 

Q20:

Consider the matrices Find 𝐴 𝐡 , if possible.

  • A ( 2 2 )
  • B ( 3 0 )
  • C  βˆ’ 4 1 2 1 4 
  • D ( βˆ’ 4 1 2 1 4 )

Q21:

Given that determine 𝐴 𝐡 if possible.

  • Aundefined
  • B  βˆ’ 1 5 4 2 2 5 
  • C  βˆ’ 1 5 4 2 1 0 5 
  • D  βˆ’ 1 5 βˆ’ 6 βˆ’ 1 4 5 

Q22:

Given that find the value of √ π‘₯ 𝑦 .

  • A9
  • B 9 √ 5
  • C 6 √ 1 0
  • D 6 √ 2

Q23:

Let , .

Verify that if matrix satisfies , then and . Find matrices and so that , and then use this to find and so that

  • A , .
  • B , .
  • C , .
  • D , .
  • E , .

Q24:

Find the values of π‘₯ and 𝑦 given

  • A π‘₯ = 5 , 𝑦 = 0
  • B π‘₯ = 1 8 , 𝑦 = βˆ’ 4 0
  • C π‘₯ = 5 , 𝑦 = βˆ’ 4 0
  • D π‘₯ = 7 , 𝑦 = βˆ’ 1 2

Q25:

Given that where 𝑂 is the zero matrix of order 2 Γ— 2 , find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 1 , 𝑦 = βˆ’ 9
  • B π‘₯ = βˆ’ 4 , 𝑦 = 1
  • C π‘₯ = βˆ’ 8 , 𝑦 = βˆ’ 9
  • D π‘₯ = βˆ’ 3 , 𝑦 = βˆ’ 1
Preview