CUET CUET Mathematics 2024 - If A=[arrayll2 & 4 \\ 4 & 3array], X=[arrayln \\ 1array], B=[arrayc8 \\ 11array] and A X=B, then the value of n will be : | PYQs + Solutions | AfterBoards
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CUET Mathematics 2024

Algebra
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Matrices & Determinants

Easy

If A=[2443],X=[n1],B=[811]\mathrm{A}=\left[\begin{array}{ll}2 & 4 \\ 4 & 3\end{array}\right], \mathrm{X}=\left[\begin{array}{l}\mathrm{n} \\ 1\end{array}\right], \mathrm{B}=\left[\begin{array}{c}8 \\ 11\end{array}\right] and AX=BA X=B, then the value of nn will be :

Correct Option: 3
A=[2443],X=[n1],B=[811]A = \left[\begin{array}{ll}2 & 4 \\ 4 & 3\end{array}\right], X = \left[\begin{array}{l}n \\ 1\end{array}\right], B = \left[\begin{array}{c}8 \\ 11\end{array}\right]
The equation is: \newline AX=BAX = B
Expanding this: \newline [2443][n1]=[811]\left[\begin{array}{ll}2 & 4 \\ 4 & 3\end{array}\right] \left[\begin{array}{l}n \\ 1\end{array}\right] = \left[\begin{array}{c}8 \\ 11\end{array}\right]
Performing the matrix multiplication: \newline [2n+44n+3]=[811]\left[\begin{array}{c}2n + 4 \\ 4n + 3\end{array}\right] = \left[\begin{array}{c}8 \\ 11\end{array}\right]
This gives us two equations: \newline 2n+4=82n + 4 = 8 \newline 4n+3=114n + 3 = 11
From the first equation: \newline 2n=42n = 4 \newline n=2n = 2
Let's verify with the second equation: \newline 4(2)+3=8+3=114(2) + 3 = 8 + 3 = 11
The value of n is 2.

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