Worksheet: Power of a Matrix

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

Q1:

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

Q2:

Which of the following represents a matrix 𝐴 such that 𝐴=𝐼, yet 𝐴𝐼 and 𝐴𝐼?

  • A𝐴=100010001
  • B𝐴=111111111
  • C𝐴=111010110
  • D𝐴=100010110
  • E𝐴=100010111

Q3:

For 𝐴=4545, write 𝐴 as a multiple of 𝐴.

  • A4𝐴
  • B𝐴
  • C4𝐴
  • D𝐴
  • E2𝐴

Q4:

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

  • A(𝐴+𝐵)=𝐴+2𝐵𝐴+𝐵
  • B(𝐴+𝐵)=𝐴+3𝐴𝐵+3𝐴𝐵+𝐵
  • C(𝐴+𝐵)=𝐴+2𝐴𝐵+𝐵
  • D(𝐴+𝐵)=𝐴+𝐴𝐵+𝐵𝐴+𝐵
  • E(𝐴𝐵)=𝐴2𝐴𝐵+𝐵

Q5:

Consider 𝑋=3356,𝑌=1366. What is 𝑋𝑌?

  • A25573033
  • B25154233
  • C25421533
  • D25305733

Q6:

Given that 𝐴=6155, find 𝐴.

  • A311520
  • B37353550
  • C315120
  • D61313126

Q7:

Given the matrix 𝐴=4037, calculate 𝐴3𝐴.

  • A160378196
  • B480246294
  • C160180196
  • D480312294

Q8:

Take the matrix 𝐴=100050002.

Find 𝐴.

  • A1000250004
  • B1111251114
  • C2222102224
  • D2000100004
  • E1222252224

Find 𝐴.

  • A13331253338
  • B3333153336
  • C11111251118
  • D3000150006
  • E10001250008

Q9:

Take the matrix 𝐴=2003.

Find 𝐴.

  • A2003
  • B4009
  • C4006
  • D6009

Find 𝐴.

  • A4006
  • B83327
  • C2003
  • D6009
  • E80027

Q10:

If 𝐴=𝑎000𝑏000𝑐, find 𝐴.

  • A𝑎111𝑏111𝑐
  • B𝑎000𝑏000𝑐
  • C𝑎222𝑏222𝑐
  • D2𝑎0002𝑏0002𝑐
  • E2𝑎2222𝑏2222𝑐

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