Matrix, in which there is a column of 0's or a row of 0's

In summary, neglecting a row or column of 0's in an n x m matrix may be equivalent when solving a system of equations, but it changes the properties of the matrix and may affect solutions when finding the nullspace.
  • #1
Gear300
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Given an n x m matrix, in which there is a column of 0's or a row of 0's, would it be equivalent to write the matrix while neglecting the column or row of 0's?
 
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  • #2


What do you mean by "equivalent"? If, for example, you were asked to the nullspace of a matrix, obviously, a row of 0's gives a solution that you would not get if you neglected that row.
 
  • #3


If you are using a matrix to solve a system of equations (like one would do in a beginners linear algebra course), then you may skip writing rows of zeroes since they give you no information. But in general, you should not skip a row or column of zeroes since it changes the properties of the matrix (as mentioned above)
 
  • #4


I see. Thanks for the replies.
 

FAQ: Matrix, in which there is a column of 0's or a row of 0's

What is a matrix with a column of 0's or a row of 0's?

A matrix is a rectangular array of numbers or symbols arranged in rows and columns. When a column or row of a matrix contains all 0's, it is called a zero matrix.

What is the significance of a zero matrix?

A zero matrix is significant because it has unique properties that distinguish it from other matrices. For example, multiplying any matrix by a zero matrix results in a zero matrix. Additionally, a zero matrix is always singular and has a determinant of 0.

Can a matrix have more than one column of 0's or row of 0's?

Yes, a matrix can have multiple columns or rows of 0's. The number of 0's in a matrix does not affect its properties, as long as there is at least one column or row of 0's.

What is the difference between a zero matrix and an empty matrix?

A zero matrix contains all 0 entries, while an empty matrix has no entries at all. An empty matrix is technically not considered a matrix because it does not have any rows or columns. However, it is often represented as a matrix with 0 rows and 0 columns.

How is a zero matrix used in mathematics and science?

A zero matrix is used in various mathematical operations, such as solving systems of linear equations and performing matrix transformations. In science, it can be used to represent situations where there is no change or effect on a system. It also has applications in computer graphics and data analysis.

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