zi2lalZ

2021-02-09

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

cyhuddwyr9

Skilled2021-02-10Added 90 answers

Step 1

Consider a square matrix $A=\left[\begin{array}{ccc}0& 0& 0\\ 1& 2& 3\\ 4& 5& 6\end{array}\right]$ and $B=\left[\begin{array}{ccc}1& 4& 0\\ 2& 5& 0\\ 3& 6& 0\end{array}\right]$

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

Expert2022-01-30Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Expert2022-08-23Added 2605 answers

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