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Lesson: Equality of Two Matrices

In this lesson, we will learn how to check the equality of matrices and how to find values of unknown variables represented as elements in two equal matrices.

Worksheet • 18 Questions

Q1:

Given that 𝐴 =  3 3 3 3 3 3  and that 𝐡 =  3 3 3 3  , is it true that 𝐴 = 𝐡 ?

  • Ayes
  • Bno

Q2:

Given that 𝐴 =  7 7 7 7 7 7  and that 𝐡 =  7 7 7 7  , is it true that 𝐴 β‰  𝐡 ?

  • Ano
  • Byes

Q3:

Given that 𝐴 =  2 2 2 2 2 2  and that 𝐡 =  2 2 2 2  , is it true that 𝐴 β‰  𝐡 ?

  • Ano
  • Byes

Q4:

Given that 𝐴 =  βˆ’ 3 βˆ’ 3 βˆ’ 3 βˆ’ 3 βˆ’ 3 βˆ’ 3  and that 𝐡 =  βˆ’ 3 βˆ’ 3 βˆ’ 3 βˆ’ 3  , is it true that 𝐴 = 𝐡 ?

  • Ayes
  • Bno

Q5:

Given that find the value of .

  • A12
  • B
  • C9
  • D2
  • E

Q6:

Given that find the value of .

  • A
  • B
  • C7
  • D2
  • E

Q7:

Given that determine the values of , , , and .

  • A , , ,
  • B , , ,
  • C , , ,
  • D , , ,

Q8:

Given that find the values of and .

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

Q9:

Given that determine the values of and .

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

Q10:

If is it true that ?

  • Ayes
  • Bno

Q11:

If is it true that ?

  • Ayes
  • Bno

Q12:

Given that find the values of , , , and .

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

Q13:

Consider the matrices and . Given that , determine the values of , , and .

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

Q14:

Given the following, find the values of and .

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

Q15:

For which of the following matrices is 𝐴 𝐡 = 𝐴 𝐢 ?

  • A 𝐴 =  1 βˆ’ 1 βˆ’ 1 1  , 𝐡 =  1 1 1 1  , 𝐢 =  2 2 2 2 
  • B 𝐴 =  1 1 1 1  , 𝐡 =  βˆ’ 1 βˆ’ 1 βˆ’ 1 βˆ’ 1  , 𝐢 =  βˆ’ 1 1 1 βˆ’ 1 
  • C 𝐴 =  1 βˆ’ 1 βˆ’ 1 1  , 𝐡 =  1 1 1 1  , 𝐢 =  2 1 1 2 
  • D 𝐴 =  1 1 1 1  , 𝐡 =  βˆ’ 1 βˆ’ 1 βˆ’ 1 βˆ’ 1  , 𝐢 =  2 2 2 2 
  • E 𝐴 =  1 βˆ’ 1 βˆ’ 1 1  , 𝐡 =  βˆ’ 1 1 1 βˆ’ 1  , 𝐢 =  2 2 2 2 

Q16:

Consider the linear transformation 𝐿 ∢ ℝ β†’ ℝ 3 3 , where 𝐿 rotates each vector 90 degrees about the positive π‘₯ -axis. Find the matrix representation of 𝐿 in the standard basis.

  • A  1 0 0 0 0 βˆ’ 1 0 1 0 
  • B  1 0 0 0 0 1 0 1 0 
  • C  1 0 0 0 0 βˆ’ 1 0 βˆ’ 1 0 
  • D  1 0 0 1 0 βˆ’ 1 1 1 0 

Q17:

Given that is it true that ?

  • Ano
  • Byes

Q18:

Given that find the values of and .

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