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

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

Q1:

Given that 𝐴=−61−55, find 𝐴.

  • A31−1520
  • B37353550
  • C315−120
  • D61−31−3126

Q2:

Consider 𝑋=−3−35−6,𝑌=136−6. What is 𝑋−𝑌?

  • A−2557−30−33
  • B−25−1542−33
  • C−2542−15−33
  • D−25−3057−33

Q3:

Given the matrix 𝐴=40−37, calculate 𝐴−3𝐴.

  • A160−378196
  • B480−246294
  • C160−180196
  • D480−312294

Q4:

Consider the matrix 𝐴=112101210.

Find 𝐴.

  • A𝐴=114101410
  • B𝐴=114101410
  • C𝐴=633322325
  • D𝐴=633312315
  • E𝐴=224202420

Find 𝐴.

  • A𝐴=336303630
  • B𝐴=159159581588
  • C𝐴=336303630
  • D𝐴=159159581588
  • E𝐴=118101810

Q5:

For 𝐴=4−54−5, write 𝐴 as a multiple of 𝐴.

  • A4𝐴
  • B𝐴
  • C−4𝐴
  • D−𝐴
  • E2𝐴

Q6:

If 𝐴=0220, which of the following is 𝐴?

  • A20220
  • B21001
  • C20220
  • D20220
  • E21001

Q7:

Which of the following statements is true for all 𝑛×𝑛 matrices 𝐴 and 𝐵?

  • A𝐴𝐵=𝐴(𝐴𝐵)𝐵
  • B(𝐴−𝐵)=𝐴−2𝐴𝐵+𝐵
  • C(𝐴𝐵)=𝐴𝐵
  • D(𝐴+𝐵)(𝐴−𝐵)=𝐴−𝐵
  • E(𝐴+𝐵)=𝐴+2𝐴𝐵+𝐵

Q8:

Fill in the blank: If 𝐴=403−4, then 𝐴=.

  • A21001
  • B21001
  • C21001
  • D21001

Q9:

Given that 𝑀=56−5−4, find the values of 𝑥 and 𝑦 that satisfy 𝑀+𝑥𝑀+𝑦𝐼=𝑂, where 𝑂 is the zero matrix of order 2×2 and 𝐼 is the unit matrix of order 2×2.

  • A𝑥=−1, 𝑦=10
  • B𝑥=−1, 𝑦=0
  • C𝑥=−11, 𝑦=0
  • D𝑥=−11, 𝑦=10

Q10:

Consider the matrices 𝐴=0−421,𝐵=−3−766−43,𝐶=77−72−77. Determine the matrix 𝑋 that satisfies −𝑋=𝐴+(𝐵𝐶).

  • A22−51−3−48
  • B22−9−45−48
  • C22−3−51−48
  • D22−45−9−48

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

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