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Lesson Worksheet: Power of a Matrix Mathematics • 10th Grade

In this worksheet, we will practice using the matrix multiplication to determine the square and cube of a square matrix.

Q1:

Given that ๐ด=๏”โˆ’61โˆ’55๏ , find ๐ด๏Šจ.

  • A๏”31โˆ’1520๏ 
  • B๏”37353550๏ 
  • C๏”315โˆ’120๏ 
  • D๏”61โˆ’31โˆ’3126๏ 

Q2:

Consider ๐‘‹=๏”โˆ’3โˆ’35โˆ’6๏ ,๐‘Œ=๏”136โˆ’6๏ . What is ๐‘‹โˆ’๐‘Œ๏Šจ๏Šจ?

  • A๏”โˆ’2557โˆ’30โˆ’33๏ 
  • B๏”โˆ’25โˆ’1542โˆ’33๏ 
  • C๏”โˆ’2542โˆ’15โˆ’33๏ 
  • D๏”โˆ’25โˆ’3057โˆ’33๏ 

Q3:

Given the matrix ๐ด=๏”40โˆ’37๏ , calculate ๐ดโˆ’3๐ด๏Šฉ๏Šจ.

  • A๏”160โˆ’378196๏ 
  • B๏”480โˆ’246294๏ 
  • C๏”160โˆ’180196๏ 
  • D๏”480โˆ’312294๏ 

Q4:

Consider the matrix ๐ด=๏˜112101210๏ค.

Find ๐ด๏Šจ.

  • A๐ด=๏˜114101410๏ค๏Šจ
  • B๐ด=๏˜114101410๏ค๏Šจ
  • C๐ด=๏˜633322325๏ค๏Šจ
  • D๐ด=๏˜633312315๏ค๏Šจ
  • E๐ด=๏˜224202420๏ค๏Šจ

Find ๐ด๏Šฉ.

  • A๐ด=๏˜336303630๏ค๏Šฉ
  • B๐ด=๏˜159159581588๏ค๏Šฉ
  • C๐ด=๏˜336303630๏ค๏Šฉ
  • D๐ด=๏˜159159581588๏ค๏Šฉ
  • E๐ด=๏˜118101810๏ค๏Šฉ

Q5:

For ๐ด=๏”4โˆ’54โˆ’5๏ , write ๐ด๏Šจ as a multiple of ๐ด.

  • A4๐ด
  • B๐ด
  • Cโˆ’4๐ด
  • Dโˆ’๐ด
  • E2๐ด

Q6:

If ๐ด=๏”0220๏ , which of the following is ๐ด๏Šฏ๏Šฏ?

  • A2๏”0220๏ ๏Šง๏Šฆ๏Šฆ
  • B2๏”1001๏ ๏Šฏ๏Šฏ
  • C2๏”0220๏ ๏Šฏ๏Šฏ
  • D2๏”0220๏ ๏Šฏ๏Šฎ
  • E2๏”1001๏ ๏Šฏ๏Šฎ

Q7:

Which of the following statements is true for all ๐‘›ร—๐‘› matrices ๐ด and ๐ต?

  • A๐ด๐ต=๐ด(๐ด๐ต)๐ต๏Šจ๏Šจ
  • B(๐ดโˆ’๐ต)=๐ดโˆ’2๐ด๐ต+๐ต๏Šจ๏Šจ๏Šจ
  • C(๐ด๐ต)=๐ด๐ต๏Šจ๏Šจ๏Šจ
  • D(๐ด+๐ต)(๐ดโˆ’๐ต)=๐ดโˆ’๐ต๏Šจ๏Šจ
  • E(๐ด+๐ต)=๐ด+2๐ด๐ต+๐ต๏Šจ๏Šจ๏Šจ

Q8:

Fill in the blank: If ๐ด=๏”403โˆ’4๏ , then ๐ด=๏Šซ๏Šฆ.

  • A2๏”1001๏ ๏Šญ๏Šซ
  • B2๏”1001๏ ๏Šซ๏Šฆ
  • C2๏”1001๏ ๏Šง๏Šฆ๏Šฆ
  • D2๏”1001๏ ๏Šจ๏Šซ

Q9:

Given that ๐‘€=๏”56โˆ’5โˆ’4๏ , find the values of ๐‘ฅ and ๐‘ฆ that satisfy ๐‘€+๐‘ฅ๐‘€+๐‘ฆ๐ผ=๐‘‚๏Šจ, where ๐‘‚ is the zero matrix of order 2ร—2 and ๐ผ is the unit matrix of order 2ร—2.

  • A๐‘ฅ=โˆ’1, ๐‘ฆ=10
  • B๐‘ฅ=โˆ’1, ๐‘ฆ=0
  • C๐‘ฅ=โˆ’11, ๐‘ฆ=0
  • D๐‘ฅ=โˆ’11, ๐‘ฆ=10

Q10:

Consider the matrices ๐ด=๏”0โˆ’421๏ ,๐ต=๏”โˆ’3โˆ’766โˆ’43๏ ,๐ถ=๏˜77โˆ’72โˆ’77๏ค. Determine the matrix ๐‘‹ that satisfies โˆ’๐‘‹=๐ด+(๐ต๐ถ)๏Œณ๏Šจ๏Œณ.

  • A๏”22โˆ’51โˆ’3โˆ’48๏ 
  • B๏”22โˆ’9โˆ’45โˆ’48๏ 
  • C๏”22โˆ’3โˆ’51โˆ’48๏ 
  • D๏”22โˆ’45โˆ’9โˆ’48๏ 

This lesson includes 32 additional questions and 225 additional question variations for subscribers.

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