Question

In a matrix a11=2,
a12=4, a21=5, a22= 10 then that matrix is called as ….. Matrix

Answer 1

The matrix is called as singular matrix

Given :

$\sf a_{11} = 2 \: , \: a_{12} = 4\:,a_{21} = 5 \:,a_{22} =10$

To find :

The matrix is called as _____ matrix

Solution :

Step 1 of 4 :

Write down the given elements

Here it is given that

$\sf a_{11} = 2 \: , \: a_{12} = 4\:,a_{21} = 5 \:,a_{22} =10$

Step 2 of 4 :

Find the matrix

Let A be the matrix obtained

Then we have

$\displaystyle A = \begin{pmatrix} \sf \: a_{11} & \sf \: a_{12}\\ \sf \: a_{21} & \sf \: a_{22} \end{pmatrix}$

$\displaystyle = \begin{pmatrix} \sf \: 2 & \sf \: 4\\ \sf \: 5& \sf \: 10 \end{pmatrix}$

Step 3 of 4 :

Find determinant value of the matrix

The determinant value of the matrix A

= det A

$\displaystyle = \begin{vmatrix} \sf \: 2 & \sf \: 4\\ \sf \: 5& \sf \: 10 \end{vmatrix}$

$\displaystyle \sf{ = (2 \times 10) - (5 \times 4) }$

$\displaystyle \sf{ = 20 - 20 }$

$\displaystyle \sf{ = 0 }$

Step 4 of 4 :

Identify the matrix

Since determinant value of the matrix is zero

So the given matrix is a singular matrix.

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