Matrices
NCERT Class 12
CBSE
Grade 12
Question:
If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$, prove that $A^2 - 4A - 5I = O$.
Step-by-Step Solution
$A^2 = \begin{bmatrix} 9 & 8 & 8 \\ 8 & 9 & 8 \\ 8 & 8 & 9 \end{bmatrix}$. [1.5 Marks]
$A^2 - 4A - 5I = \begin{bmatrix} 9-4-5 & 8-8-0 & 8-8-0 \\ 8-8-0 & 9-4-5 & 8-8-0 \\ 8-8-0 & 8-8-0 & 9-4-5 \end{bmatrix} = O$. Proved! [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Evaluating matrix square $A^2$: 1.5 Marks
Evaluating matrix polynomial $A^2 - 4A - 5I = O$: 1.5 Marks
Correct Answer:
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