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Worksheet: Rank of a Matrix by Echelon Form

Q1:

Find the rank of the matrix

Q2:

Find the rank of the matrix

Q3:

Find the rank of the matrix

Q4:

If 𝐴 is an 𝑛 Γ— 𝑛 matrix of rank 𝑝 < 𝑛 ,then what is the dimension of the null-space of 𝐴 .

  • A 𝑛 βˆ’ 𝑝 + 1
  • B 𝑝
  • C0
  • D 𝑛 βˆ’ 𝑝
  • EIt cannot be determined from the data.

Q5:

Find the rank of the matrix .

Q6:

Find the rank of the matrix .

Q7:

Find the rank of the matrix .

Q8:

Find the rank of the matrix

  • A4
  • B2
  • C7
  • D3
  • E5

Q9:

What is the rank of the matrix ?

Q10:

What is the rank of the matrix ?

Q11:

What is the rank of the matrix ?