NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 7

Question

Find X,Y for (i) X+Y=$\left[\begin{matrix}7 & 0\2 & 5\end{matrix}\right]$, X−Y=$\left[\begin{matrix}3 & 0\0 & 3\end{matrix}\right]$; (ii) 2X+3Y=$\left[\begin{matrix}2 & 3\4 & 0\end{matrix}\right]$, 3X+2Y=$\left[\begin{matrix}2 & -2\-1 & 5\end{matrix}\right]$.

Accepted Answer

Final Answer: (i) X = $\left[\begin{matrix}5 & 0\1 & 4\end{matrix}\right]$, Y = $\left[\begin{matrix}2 & 0\1 & 1\end{matrix}\right]$; (ii) X = $\left[\begin{matrix}\frac{2}{5} & - \frac{12}{5}\- \frac{11}{5} & 3\end{matrix}\right]$, Y = $\left[\begin{matrix}\frac{2}{5} & \frac{13}{5}\\frac{14}{5} & -2\end{matrix}\right]$ Step 1: (i) Add and subtract the equations: 2X=A+B, 2Y=A−B. Hence X = $\left[\begin{matrix}5 & 0\1 & 4\end{matrix}\right]$, Y = $\left[\begin{matrix}2 & 0\1 & 1\end{matrix}\right]$. Step 2: (ii) Eliminate Y: 3(3X+2Y)−2(2X+3Y)=5X=3B−2A. Eliminate X: 3(2X+3Y)−2(3X+2Y)=5Y=3A−2B. Step 3: Thus X = $\left[\begin{matrix}\frac{2}{5} & - \frac{12}{5}\- \frac{11}{5} & 3\end{matrix}\right]$, Y = $\left[\begin{matrix}\frac{2}{5} & \frac{13}{5}\\frac{14}{5} & -2\end{matrix}\right]$. Substitute in both equations to verify.

NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 7

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