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Worksheet: Rank of a Matrix by Determinant

Q1:

What value can not take if the rank of the following matrix is 3?

Q2:

What value can not take if the rank of the following matrix is 3?

Q3:

Find the rank of

  • A2
  • B3
  • C5
  • D4
  • E6

Q4:

If the matrix has rank 2, what is the value of ?

Q5:

If the matrix has rank 2, what is the value of ?

Q6:

What is the rank of the identity matrix, ๐ผ 3 ?

Q7:

What is the rank of the zero matrix of order 3 ร— 3 ?

Q8:

What is the rank of the zero matrix of order 2 ร— 2 ?

Q9:

Determine the value of that makes the following matrix have the lowest rank possible.

Q10:

What is the rank of the identity matrix, ๐ผ 2 ?

Q11:

Determine the rank of the following matrix for all real values of .

  • AWhen , , and when ,
  • BWhen , , and when ,
  • CWhen , , and when ,
  • DWhen , , and when ,