# Worksheet: Rank of a Matrix

In this worksheet, we will practice finding the rank and nullity of a matrix.

Q1:

What is the rank of the matrix ?

Q2:

Find the rank of the matrix .

Q3:

Find the rank of the matrix

Q4:

Find the rank of the matrix

Q5:

Find the rank of the matrix

Q6:

Find the rank of the matrix

Q7:

If is an matrix of rank ,then what is the dimension of the null-space of .

• A
• B
• CIt cannot be determined from the data.
• D
• E0

Q8:

Find the rank of the matrix .

Q9:

Find the rank of the matrix .

Q10:

What is the rank of the matrix ?

Q11:

What is the rank of the matrix ?

Q12:

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

Q13:

Find the rank of

Q14:

Find the rank of the matrix

Q15:

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

Q16:

What is the rank of the identity matrix, ?

Q17:

What is the rank of the zero matrix of order ?

Q18:

What is the rank of the zero matrix of order ?

Q19:

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

Q20:

What is the rank of the identity matrix, ?

Q21:

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

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

Q22:

Find the rank of the augmented matrix of the following system of equations:

Q23:

Find the rank of the augmented matrix of the following system of equations:

Q24:

Determine the order of an augmented matrix that represents linear equations in variables.

• A
• B
• C
• D

Q25:

Suppose , and are invertible matrices. Which of the following is false?

• A does not have full rank.
• B is invertible.
• C
• D