
If $\left[ \begin{matrix}
m & n \\
\end{matrix} \right]$$\left[ \begin{matrix}
m \\
n \\
\end{matrix} \right]$= $\left[ 25 \right]$ and m < n, then $\left[ m,n \right]$ =
A . $\left[ 2,3 \right]$
B . $\left[ 3,4 \right]$
C . $\left[ 4,3 \right]$
D . None of these
Answer
163.5k+ views
Hint: In this question, we have given matrices in the form of m and n and we have to find the value of m and n. First we multiply both the matrix and then by putting the values of m and n which are given in the options, check whether which value of m and n satisfies the given equation and choose the correct option.
Complete Step- by- step Solution:
Given $\left[ \begin{matrix}
m & n \\
\end{matrix} \right]$$\left[ \begin{matrix}
m \\
n \\
\end{matrix} \right]$= $\left[ 25 \right]$
First we multiply the matrices, we get
${{m}^{2}}+\,{{n}^{2}}=25$…………………………………… [1]
Now we use the options to find the value of m and n.
We put the values of m and n is equation [1] and check whether which value satisfies the equation.
First let $m=2,n=3$
Then ${{[2]}^{2}}+\,{{[3]}^{2}}=25$
Solving further, we get
$13\ne 25$
Then we put $m=3,n=4$
Then ${{[3]}^{2}}+\,{{[4]}^{2}}=25$
Hence $25=25$
In option [ C ] where $m=4,n=3$
But in this question, we have given m < n
So $m=4,n=3$ value does not possible.
After checking put all the options, we found that the value of $\left[ m,n \right]$ = $\left[ 3,4 \right]$
Thus, Option [ B ] is the correct answer.
Note: In these types of questions, Students male mistakes in multiplying the matrices. In multiplication of matrices, if we take $A[4\times 3]$ and $B[3\times 4]$ multiplication of both the matrix is possible but If we take $A[4\times 3]$ and $B[4\times 3]$ multiplication of matrices is not possible.
Complete Step- by- step Solution:
Given $\left[ \begin{matrix}
m & n \\
\end{matrix} \right]$$\left[ \begin{matrix}
m \\
n \\
\end{matrix} \right]$= $\left[ 25 \right]$
First we multiply the matrices, we get
${{m}^{2}}+\,{{n}^{2}}=25$…………………………………… [1]
Now we use the options to find the value of m and n.
We put the values of m and n is equation [1] and check whether which value satisfies the equation.
First let $m=2,n=3$
Then ${{[2]}^{2}}+\,{{[3]}^{2}}=25$
Solving further, we get
$13\ne 25$
Then we put $m=3,n=4$
Then ${{[3]}^{2}}+\,{{[4]}^{2}}=25$
Hence $25=25$
In option [ C ] where $m=4,n=3$
But in this question, we have given m < n
So $m=4,n=3$ value does not possible.
After checking put all the options, we found that the value of $\left[ m,n \right]$ = $\left[ 3,4 \right]$
Thus, Option [ B ] is the correct answer.
Note: In these types of questions, Students male mistakes in multiplying the matrices. In multiplication of matrices, if we take $A[4\times 3]$ and $B[3\times 4]$ multiplication of both the matrix is possible but If we take $A[4\times 3]$ and $B[4\times 3]$ multiplication of matrices is not possible.
Recently Updated Pages
JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

JEE Isolation, Preparation and Properties of Non-metals Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Degree of Dissociation and Its Formula With Solved Example for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Instantaneous Velocity - Formula based Examples for JEE

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

JEE Advanced 2025 Notes

JEE Main Chemistry Question Paper with Answer Keys and Solutions

Total MBBS Seats in India 2025: Government and Private Medical Colleges

NEET Total Marks 2025
