Answer
385.2k+ views
Hint: Every square matrix A is associated with a number called a determinant and it is denoted by $\det \left( A \right)$ or $\left| A \right|$ . Only square matrices have determinants. Matrices which are not square will not have any determinants. Square matrices are those which have an equal number of rows and columns. We usually see first order determinant, second order determinant and third order determinant. But there are many more.
Complete step-by-step answer:
Let’s first how to find the determinant of a square matrix of order 1 :
$\Rightarrow $ If A = $\left[ a \right]$ then $\det \left( A \right)=\left| A \right|=a$ . It has only one element in it which is $a$ .
Elements are the numbers written inside the matrix.
Now let’s see how to find the determinant of a square matrix of order 2 :
$\Rightarrow $ If A = $\left[ \begin{matrix}
{{a}_{11}} & {{a}_{12}} \\
{{a}_{21}} & {{a}_{22}} \\
\end{matrix} \right]$ then $\det \left( A \right)=\left| A \right|={{a}_{11}}{{a}_{22}}-{{a}_{21}}{{a}_{12}}$
In the question , we can clearly see that we got a square matrix of order 2 .
Let’s apply the formula which we have just seen.
Let’s consider the given matrix to be B.
B = $\left| \begin{matrix}
4 & -1 \\
-2 & 3 \\
\end{matrix} \right|$ . Let’s compare this with the standard matrix A.
Upon comparing, we conclude the following :
$\begin{align}
& \Rightarrow {{a}_{11}}=4 \\
& \Rightarrow {{a}_{12}}=-1 \\
& \Rightarrow {{a}_{21}}=-2 \\
& \Rightarrow {{a}_{22}}=3 \\
\end{align}$ $$ $$
Now let’s apply the formula which we have written in the above statements.
\[\Rightarrow \det \left( B \right)=\left| B \right|={{a}_{11}}{{a}_{22}}-{{a}_{21}}{{a}_{12}}\]
Upon applying the formula ,we get the following :
\[\Rightarrow \det \left( B \right)=\left| B \right|=4\times 3-\left( -1 \right)\times \left( -2 \right)=12-2=10\]
Det value cannot be negative.
$\therefore $ Hence $\det \left( B \right)=\left| B \right|=10$
Note: Please be careful while comparing the elements with the standard form . And we should also be able to identify the order of the given square matrix as the det formula for each square matrix of different order varies.
.
Complete step-by-step answer:
Let’s first how to find the determinant of a square matrix of order 1 :
$\Rightarrow $ If A = $\left[ a \right]$ then $\det \left( A \right)=\left| A \right|=a$ . It has only one element in it which is $a$ .
Elements are the numbers written inside the matrix.
Now let’s see how to find the determinant of a square matrix of order 2 :
$\Rightarrow $ If A = $\left[ \begin{matrix}
{{a}_{11}} & {{a}_{12}} \\
{{a}_{21}} & {{a}_{22}} \\
\end{matrix} \right]$ then $\det \left( A \right)=\left| A \right|={{a}_{11}}{{a}_{22}}-{{a}_{21}}{{a}_{12}}$
In the question , we can clearly see that we got a square matrix of order 2 .
Let’s apply the formula which we have just seen.
Let’s consider the given matrix to be B.
B = $\left| \begin{matrix}
4 & -1 \\
-2 & 3 \\
\end{matrix} \right|$ . Let’s compare this with the standard matrix A.
Upon comparing, we conclude the following :
$\begin{align}
& \Rightarrow {{a}_{11}}=4 \\
& \Rightarrow {{a}_{12}}=-1 \\
& \Rightarrow {{a}_{21}}=-2 \\
& \Rightarrow {{a}_{22}}=3 \\
\end{align}$ $$ $$
Now let’s apply the formula which we have written in the above statements.
\[\Rightarrow \det \left( B \right)=\left| B \right|={{a}_{11}}{{a}_{22}}-{{a}_{21}}{{a}_{12}}\]
Upon applying the formula ,we get the following :
\[\Rightarrow \det \left( B \right)=\left| B \right|=4\times 3-\left( -1 \right)\times \left( -2 \right)=12-2=10\]
Det value cannot be negative.
$\therefore $ Hence $\det \left( B \right)=\left| B \right|=10$
Note: Please be careful while comparing the elements with the standard form . And we should also be able to identify the order of the given square matrix as the det formula for each square matrix of different order varies.
.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)