NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 4

Question

For A = $\left[\begin{matrix}1 & 2 & -3\5 & 0 & 2\1 & -1 & 1\end{matrix}\right]$, B = $\left[\begin{matrix}3 & -1 & 2\4 & 2 & 5\2 & 0 & 3\end{matrix}\right]$, C = $\left[\begin{matrix}4 & 1 & 2\0 & 3 & 2\1 & -2 & 3\end{matrix}\right]$, compute A+B,B−C and verify A+(B−C)=(A+B)−C.

Accepted Answer

Final Answer: A+B = $\left[\begin{matrix}4 & 1 & -1\9 & 2 & 7\3 & -1 & 4\end{matrix}\right]$, B−C = $\left[\begin{matrix}-1 & -2 & 0\4 & -1 & 3\1 & 2 & 0\end{matrix}\right]$, both sides = $\left[\begin{matrix}0 & 0 & -3\9 & -1 & 5\2 & 1 & 1\end{matrix}\right]$ Step 1: First add/subtract entries: A+B = $\left[\begin{matrix}4 & 1 & -1\9 & 2 & 7\3 & -1 & 4\end{matrix}\right]$, B−C = $\left[\begin{matrix}-1 & -2 & 0\4 & -1 & 3\1 & 2 & 0\end{matrix}\right]$. Step 2: Then A+(B−C)=$\left[\begin{matrix}0 & 0 & -3\9 & -1 & 5\2 & 1 & 1\end{matrix}\right]$ and (A+B)−C=$\left[\begin{matrix}0 & 0 & -3\9 & -1 & 5\2 & 1 & 1\end{matrix}\right]$. Step 3: The resulting entries match, proving the identity.

NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 4

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