Worksheet: Rank of a Matrix by Echelon Form

In this worksheet, we will practice determining the rank of a matrix by transforming it to its row echelon form then counting the nonzero rows.

Q1:

What is the rank of the matrix ( 0 0 ) ?

Q2:

Find the rank of the matrix 2 2 4 4 4 8 .

Q3:

Find the rank of the given matrix.

Q4:

Find the rank of the matrix

Q5:

Find the rank of the given matrix.

Q6:

Find the rank of the following matrix.

  • A4
  • B2
  • C7
  • D3
  • E5

Q7:

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

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

Q8:

Find the rank of the matrix 2 2 2 0 5 8 2 1 2 1 .

Q9:

Find the rank of the matrix 1 0 5 4 5 0 2 5 2 0 .

Q10:

What is the rank of the matrix 7 0 0 ?

Q11:

What is the rank of the matrix ( 8 0 0 ) ?

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