COLUMN MATRIX

Column Matrix

Definition Of Column Matrix

A matrix which has only one column is called a Column Matrix.

More about Column Matrix

Sum of two column matrices of same dimension is also a column matrix of the same dimension.
If a row matrix is multiplied with a column matrix having the same number of elements, then the resultant has one element only.

Video Examples: Maths Matrices

Example of Column Matrix

example of Column Matrix

The above matrix has three rows but only one column, so it is a column matrix.

Solved Example onColumn Matrix

Ques: Which of the following is a column matrix?

Choices:

A. example of Column Matrix
B.
C.
D.
Correct Answer: B

Solution:

Step 1: A matrix which has only one column is called a Column Matrix.
Step 2: As example of Column Matrix has 3 rows and 1 column, it is a column matrix.

Quick Summary

A column matrix has dimensions m x 1, where m is the number of rows.
The sum of two column matrices of the same dimension is a column matrix of the same dimension.
Multiplying a row matrix by a column matrix (with matching dimensions) results in a scalar.

\[ A = \begin{bmatrix} a_{11} \\ a_{21} \\ \vdots \\ a_{m1} \end{bmatrix} \]

🍎 Teacher Insights

Emphasize the visual aspect of a column matrix to help students differentiate it from other types of matrices. Use examples of column matrices in real-world applications, such as representing data points or vectors.

🎓 Prerequisites

Matrix
Vector
Dimensions of a Matrix

Check Your Knowledge

Q1: Which of the following is a column matrix?

[1, 2] [1; 2] [[1, 2]] [[1], [2]]

Q2: What is the dimension of the matrix [[1], [2], [3]]?

1x3 3x1 3x3 1x1

Frequently Asked Questions

Q: What is the difference between a column matrix and a column vector?
A: They are often used interchangeably. A column vector is a specific instance of a column matrix.

Q: Can a column matrix have only one element?
A: Yes, a column matrix can have only one element, in which case it is a 1x1 matrix.