CBSE Class 12 Mathematics 2025: question 27(a)

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Step-by-step solution

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1. The equations are $2x+5y=1$ and $3x+2y=7$. In matrix form $AX=B$, where $A=\left[\begin{array}{cc}2& 5\\ 3& 2\end{array}\right]$, $X=\left[\begin{array}{c}x\\ y\end{array}\right]$, $B=\left[\begin{array}{c}1\\ 7\end{array}\right]$.

   1 mark

2. $|A|=4-15=-11\ne 0$, so $A^{-1}$ exists and $\mathrm{adj}A=\left[\begin{array}{cc}2& -5\\ -3& 2\end{array}\right]$. Then $X=A^{-1}B=-\frac{1}{11}\left[\begin{array}{cc}2& -5\\ -3& 2\end{array}\right]\left[\begin{array}{c}1\\ 7\end{array}\right]=-\frac{1}{11}\left[\begin{array}{c}-33\\ 11\end{array}\right]=\left[\begin{array}{c}3\\ -1\end{array}\right]$

   1½ marks

3. So $x=3$, $y=-1$. The point common to the paths of the ants is $(3,-1)$.

   ½ mark

Answer: (3, −1)

Revise the chapter

• Chapter: Matrices (notes, formulas, where marks are lost and every past question)