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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 224448.

Q2:

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

7𝑥+2𝑦=2,2𝑥+5𝑦=9.

Q3:

Find the rank of the following matrix using determinants: 768838.

Q4:

Find the rank of the following matrix: 124712248.

Q5:

Find the rank of the matrix 1611141719243624.

Q6:

What value can 𝑘 not take if the rank of the matrix 𝐴=741522𝑘2491521 is 3?

Q7:

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

2𝑥+4𝑦=3,2𝑥+3𝑦=6.

Q8:

Find the number of solutions for the following system of linear equations: 51112141014312𝑥𝑦𝑧=1047.

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

Q9:

Find the number of solutions for the following system of linear equations: 2019171741916915𝑥𝑦𝑧=13207.

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

Q10:

Find the number of solutions of the following system of linear equations: 126201208111412𝑥𝑦𝑧=51611.

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

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

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