Lesson Worksheet: Rank of a Matrix: Determinants Mathematics

In this worksheet, we will practice finding the rank of a matrix using determinants and how to use this to determine the number of solutions to a system of linear equations.

Q1:

Find the rank of the matrix .

Q2:

Use determinants to find the rank of the coefficient matrix of the following system of equations:

Q3:

Find the rank of the following matrix using determinants:

Q4:

Find the rank of the following matrix:

Q5:

Find the rank of the matrix

Q6:

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

Q7:

Use determinants to find the rank of the agumented matrix of the following system of equations:

Q8:

Find the number of solutions for the following system of linear equations:

• AOne solution
• BAn infinite number of solutions
• CNo solutions

Q9:

Find the number of solutions for the following system of linear equations:

• AAn infinite number of solutions
• BNo solutions
• COne solution

Q10:

Find the number of solutions of the following system of linear equations:

• AOne solution
• BNo solutions
• CAn infinite number of solutions

This lesson includes 28 additional questions and 169 additional question variations for subscribers.