Elementary Matrix Calculator

The elementary matrix calculator calculates the elementary matrix by applying the row or column operation on an identity matrix. 

What Is An Elementary Matrix?

An elementary matrix is a square matrix that is evaluated by performing the row or column operation on an identity matrix.

You need to perform the following three operations to figure out an elementary matrix:

1. Interchange the Row or Column of the identity matrix
2. Multiply the Row or Column by a non-zero constant
3. Add the multiple of one Row or Column to each other

If you are finding any difficulty to figure out the elementary matrix use the matrix elementary row operations calculator and your task simple.

Elementary Matrix Formula:

The formula for getting the elementary matrix is given:

Row Operation:

$$ aR_p + bR_q -> R_q $$   

Column Operation:

$$ aC_p + bC_q -> C_q $$ 

For applying the simple row or column operation on the identity matrix, we recommend you use the elementary matrix calculator.

Example:

Calculate the elementary matrix for the following set of values:

\(a =3\)

\(b =4\)

\(R_{p} =2\)

\(R_{q}=3\)

Given:

Matrix Size (n)= 3

Resultant Row (Rq) = 3

Pth Row (Rp) = 2

Factor a = 3

Factor b = 4

Solution:

The identity matrix of n= 3 is 

$$\begin{bmatrix} 1&0&0\\0&1&0\\0&0&1\\\end{bmatrix}$$

The formula for the row operation is:

$$ aR_p + bR_q -> R_q $$ 

Now apply the operation 

aRp = 3 x R2 (Rp is 2 nd Row)

bRq = 4 x R3 (Rq is 3 rd Row)

Then 

$$\begin{bmatrix} 1&0&0\\0&3&0\\0&0&4\\\end{bmatrix}$$

Now:

$$3R_2 + 4R_3 = aR_p + bR_q$$

$$\begin{bmatrix} 1&0&0\\0&3&0\\0&3&4\\\end{bmatrix}$$

The final elementary matrix is:

$$\begin{bmatrix} 1&0&0\\0&1&0\\0&3&4\\\end{bmatrix}$$

Our elementary row operation calculator also generates the same results but in seconds which saves a lot of time. 

Working of Elementary Matrix Calculator:

Using our calculator is quite straightforward. All you need to do is to input the following entities:

Input:

• Choose the Row or Column elementary matrix from the drop-down menu
• Enter the size of the matrix
• Enter Pth Row or Pth column
• Enter qth Row or qth column
• Enter values of “a” and “b”
• Hit the calculate Button

Output:

• The elementary matrix
• Step-by-step calculations

FAQs:

What Is the Difference Between Elementary Matrix and Identity Matrix?

The identity matrix only contains only 1 and 0, but the elementary matrix can contain any no zero numbers. An elementary matrix is actually derived from the identity matrix. 

Is the Elementary Matrix Always a Square Matrix?

Yes, the elementary matrix is always a square matrix.

Does the Row or Column Operation Produce the Same Elementary Matrix?

No, the row and column operations generate different elementary matrices. A different result is generated when you are applying the row and column operation on an identity matrix to convert it into the elementary matrix. You can easily apply the row or column operation on an identity matrix with the elementary matrices calculator.

References:

From the source of statlect.com: Elementary matrix, Definition

From the source of Wikipedia: Elementary row operations, Properties