Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

zi2lalZ 2021-02-09 Answered
Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

cyhuddwyr9
Answered 2021-02-10 Author has 90 answers
Step 1
Consider a square matrix A=[000123456] and B=[140250360]
Here, all the elements of first row of the matrix A and all the elements of third column of the matrix B are zero.
Step 2
Since, the determinant of a matrix is zero if all the elements of a row or column are zero.
Therefore, |A|=0 and |B|=0
If the determinant of a matrix is zero then the matrix is called singular matrix.
Hence, the square matrices A and B are singular.
Not exactly what you’re looking for?
Ask My Question
Jeffrey Jordon
Answered 2022-01-30 Author has 2047 answers

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more