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Lesson: Equality of Two 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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