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

Lesson: Matrix Operations

Sample Question Videos

Worksheet • 14 Questions • 2 Videos

Q1:

Solve for matrix 𝑋 in the matrix equation 3 𝑋 + 𝐡 = 𝐢 , where 𝐡 and 𝐢 are

  • A  1 βˆ’ 3 4 5 
  • B  6 βˆ’ 6 1 5 1 8 
  • C  3 βˆ’ 9 1 2 1 5 
  • D  0 βˆ’ 1 2 βˆ’ 1 1 βˆ’ 4 
  • E  βˆ’ 1 3 βˆ’ 4 βˆ’ 5 

Q2:

Find the sum of the following matrices.

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

Q3:

Given that what is 1 3 ( 𝐴 + 𝐡 ) ?

  • A βŽ› ⎜ ⎜ ⎝ βˆ’ 2 5 3 1 βˆ’ 4 3 ⎞ ⎟ ⎟ ⎠
  • B ο€Ό βˆ’ 6 5 3 βˆ’ 4 
  • C ο€Ό βˆ’ 6 1 2 βˆ’ 4 βˆ’ 4 
  • D  βˆ’ 2 4 βˆ’ 4 3 βˆ’ 4 3 

Q4:

Given that find 𝐴 𝑇 .

  • A  βˆ’ 2 1 6 8 βˆ’ 6 4 
  • B  1 βˆ’ 2 8 6 4 βˆ’ 6 
  • C ο€½ 1 8 4 βˆ’ 2 6 βˆ’ 6 
  • D  βˆ’ 6 4 6 8 βˆ’ 2 1 

Q5:

If and , is ?

  • Ano
  • Byes

Q6:

Suppose that , , and .

Find .

  • A
  • B
  • C
  • D
  • E

Find .

  • A
  • B
  • C
  • D
  • E

Find .

  • A
  • B
  • C
  • D
  • E

Express in terms of and .

  • A
  • B
  • C
  • D
  • E

Q7:

Consider the matrices

Find ο€Ή 𝐴 + 𝐡  ο€Ή 𝐴 βˆ’ 𝐡  𝑇 𝑇 .

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

Q8:

Given that determine ο€Ή 𝐴 𝐡  𝑇 𝑇 .

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

Q9:

Given that determine the matrix 𝐡 .

  • A  βˆ’ 8 βˆ’ 5 1 0 1 1 5 βˆ’ 3 6 1 βˆ’ 1 
  • B  βˆ’ 8 βˆ’ 6 1 1 1 2 5 βˆ’ 6 5 4 βˆ’ 1 
  • C  βˆ’ 8 1 1 6 βˆ’ 5 5 1 1 0 βˆ’ 3 βˆ’ 1 
  • D  βˆ’ 8 1 2 5 βˆ’ 6 5 4 1 1 βˆ’ 6 βˆ’ 1 

Q10:

Given that find the result of 𝐴 βˆ’ 𝐡 𝑇 , if possible.

  • A ο€Ό βˆ’ 1 4 2 6 1 0 βˆ’ 4 1 2 
  • B  1 4 βˆ’ 1 0 βˆ’ 2 4 βˆ’ 6 βˆ’ 1 2 
  • CIt is not possible.
  • D ο€Ό 1 4 βˆ’ 2 βˆ’ 6 βˆ’ 1 0 4 βˆ’ 1 2 
  • E  βˆ’ 1 4 1 0 2 βˆ’ 4 6 1 2 

Q11:

If and then which of the following cannot exist?

  • A
  • B
  • C
  • D

Q12:

Given that the order of the matrix 𝐴 is 2 Γ— 2 , and that of the matrix 𝐡 𝑇 is 1 Γ— 2 , which of the following operations can be performed?

  • A 𝐴 Γ— 𝐡
  • B 𝐴 + 𝐡
  • C 𝐴 Γ— 𝐡 𝑇
  • D 𝐴 + 𝐡 𝑇 𝑇

Q13:

𝐽 and 𝐾 are two matrices with the property that for any 3 Γ— 3 matrix 𝑋 , 𝐽 𝑋 = 𝑋 and 𝑋 𝐾 = 𝑋 . Are 𝐽 and 𝐾 equal?

  • A No, they have different dimensions.
  • B Yes, they are both the 3 Γ— 3 identity matrix.
  • C No, they are different matrices of the same dimensions.

Q14:

𝐽 and 𝐾 are two matrices with the property that for any 2 Γ— 3 matrix 𝑋 , 𝐽 𝑋 = 𝑋 and 𝑋 𝐾 = 𝑋 . Are 𝐽 and 𝐾 equal?

  • A Yes, they are both the identity matrix.
  • B No, they have different dimensions.
  • C No, they are different matrices of the same dimensions.
Preview