Question
Download Solution PDF\(A = \begin{bmatrix} 2 & 3\\ -1& 2 \end{bmatrix} \)అయితే, A2 - 4A + 7I విలువను కనుగొనండి.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFగణన:
ఇవ్వబడింది: A = \(\begin{bmatrix} 2&3 \\ -1 &2 \end{bmatrix}\)
కనుగొనాల్సినది: A2 - 4A + 7I
A2 - 4A + 7I = \(\begin{bmatrix} 2&3 \\ -1 &2 \end{bmatrix}\) x \(\begin{bmatrix} 2&3 \\ -1 &2 \end{bmatrix}\) - 4\(\begin{bmatrix} 2 &3 \\ -1& 2 \end{bmatrix}\) + 7\(\begin{bmatrix} 1 &0 \\ 0& 1 \end{bmatrix}\)
= \(\begin{bmatrix} 4 - 3 &6 + 6 \\ -2 - 2& -3 + 4 \end{bmatrix}\) - \(\begin{bmatrix} 8 &12 \\ -4& 8 \end{bmatrix}\) + \(\begin{bmatrix} 7 &0 \\ 0& 7 \end{bmatrix}\)
= \(\begin{bmatrix} 1 &12 \\ -4& 1 \end{bmatrix}\)- \(\begin{bmatrix} 8 &12 \\ -4& 8 \end{bmatrix}\) + \(\begin{bmatrix} 7 &0 \\ 0& 7 \end{bmatrix}\)
= \(\begin{bmatrix} 8 &12 \\ -4& 8 \end{bmatrix}\) - \(\begin{bmatrix} 8 &12 \\ -4& 8 \end{bmatrix}\)
=\(\begin{bmatrix} 0 &0 \\ 0& 0 \end{bmatrix}\)
= 0
Last updated on May 31, 2025
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