NCERT Class 12 · Ch 3 Exercise 3.2 · Q15
NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 15
For A=\(\left[\begin{matrix}2 & 0 & 1\\2 & 1 & 3\\1 & -1 & 0\end{matrix}\right]\), compute A²−5A+6I.
💡 Concept Hints
- Check the matrix orders and the meaning of the requested operation before calculating.
- Keep row and column indices in order. Compare corresponding entries only after the matrix expressions have compatible dimensions.
✅ Step-by-Step Solution
Final Answer: \(\left[\begin{matrix}1 & -1 & -3\\-1 & -1 & -10\\-5 & 4 & 4\end{matrix}\right]\)
- Multiply A by itself: A²=\(\left[\begin{matrix}5 & -1 & 2\\9 & -2 & 5\\0 & -1 & -2\end{matrix}\right]\).
- The matrices −5A and 6I are \(\left[\begin{matrix}-10 & 0 & -5\\-10 & -5 & -15\\-5 & 5 & 0\end{matrix}\right]\) and \(\left[\begin{matrix}6 & 0 & 0\\0 & 6 & 0\\0 & 0 & 6\end{matrix}\right]\).
- Adding corresponding entries gives \(\left[\begin{matrix}1 & -1 & -3\\-1 & -1 & -10\\-5 & 4 & 4\end{matrix}\right]\).
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