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

zi2lalZ

zi2lalZ

Answered question

2021-02-09

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

Answer & Explanation

cyhuddwyr9

cyhuddwyr9

Skilled2021-02-10Added 90 answers

Step 1 
Consider a square matrix A=[000123456] and B=[140250360] 
In this case, all of the elements in the third column of the matrix B and the first row of the matrix A are zero.
Step 2 
Since all of the elements in a row or column must be zero for the determinant of a matrix to be zero.
Therefore, |A|=0 and |B|=0 
A matrix is referred to as a singular matrix if its determinant is zero.
Hence, the square matrices A and B are singular.

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-30Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-23Added 2605 answers

Answer is given below (on video)

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