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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 𝐴=6155, find 𝐴.

  • A311520
  • B37353550
  • C315120
  • D61313126

Q2:

Consider 𝑋=3356,𝑌=1366. What is 𝑋𝑌?

  • A25573033
  • B25154233
  • C25421533
  • D25305733

Q3:

Given the matrix 𝐴=4037, calculate 𝐴3𝐴.

  • A160378196
  • B480246294
  • C160180196
  • D480312294

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=4545, write 𝐴 as a multiple of 𝐴.

  • A4𝐴
  • B𝐴
  • C4𝐴
  • D𝐴
  • 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(𝐴𝐵)=𝐴2𝐴𝐵+𝐵
  • C(𝐴𝐵)=𝐴𝐵
  • D(𝐴+𝐵)(𝐴𝐵)=𝐴𝐵
  • E(𝐴+𝐵)=𝐴+2𝐴𝐵+𝐵

Q8:

Fill in the blank: If 𝐴=4034, then 𝐴=.

  • A21001
  • B21001
  • C21001
  • D21001

Q9:

Given that 𝑀=5654, 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=0421,𝐵=376643,𝐶=777277. Determine the matrix 𝑋 that satisfies 𝑋=𝐴+(𝐵𝐶).

  • A2251348
  • B2294548
  • C2235148
  • D2245948

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

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