यदि A = [ lll 1 & 3 & 3 1 & 4 & 3 1 & 3 & 4 ] हो तो सत्यापित कीजिए कि A. adj A = |A|.I और A^ -1 ज्ञात कीजिए।

|A| = 1(16 - 9) - 3(4 - 3) + 3(3 - 4) = 1 0 अब A_ 11 = 7, A_ 12 = - 1, A_ 13 = - 1, A_ 21 = - 3, A_ 22 = 1, A_ 23 = 0, A_ 31 = - 3, A_ 32 = 0, A_ 33 = 1 |A| = 1 इसलिए adj A = [ rrr -1 & 1 & 0 -1 & 0 & 1 ] अब A. (adj A) = [ lll 1 & 3 & 3 1 & 4 & 3 1 & 3 & 4 ] [ ccc 7 & -3 & -3 -1 & 1 & 0 -1 & 0 & 1 ] = [ rrr 7-3-3 & -3+3+0 & -3+0+3 7-4-3 & -3+4+0 & -3+0+3 7-3-4 & -3+3+0 & -3+0+4 ] = [ lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 ] = (1) [ lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 ] = |A|.I A-1 = 1 |~A| adj A = 11 [ ccc 7 & -3 & -3 -1 & 1 & 0 -1 & 0 & 1 ] = [ ccc 7 & -3 & -3 -1 & 1 & 0 -1 & 0 & 1 ]

यदि A = [ lll 1 & 3 & 3 1 & 4 & 3 1 & 3 & 4 ] हो तो सत्यापित कीजि…

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यदि $A = \left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{array}\right]$ हो तो सत्यापित कीजिए कि $A. adj A = |A|.I$ और $A^{-1}$ ज्ञात कीजिए।

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$|A| = 1(16 - 9) - 3(4 - 3) + 3(3 - 4) = 1 \neq 0$
अब $A_{11 }= 7, A_{12 }= - 1, A_{13 }= - 1, A_{21} = - 3, A_{22 }= 1, A_{23 }= 0, A_{31 }= - 3, A_{32 }= 0, A_{33} = 1$
$|A| = 1$
इसलिए $adj A = \left[\begin{array}{rrr} -1 & 1 & 0 \\ -1 & 0 & 1 \end{array}\right]$
अब $A. (adj A) = \left[\begin{array}{lll} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4 \end{array}\right]\left[\begin{array}{ccc} 7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end{array}\right]$
$= \left[\begin{array}{rrr} 7-3-3 & -3+3+0 & -3+0+3 \\ 7-4-3 & -3+4+0 & -3+0+3 \\ 7-3-4 & -3+3+0 & -3+0+4 \end{array}\right]$
$= \left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] = (1) \left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] = |A|.I$
$A-1 = \frac{1}{|\mathrm{~A}|} \cdot adj A = \frac 11\left[\begin{array}{ccc} 7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end{array}\right] = \left[\begin{array}{ccc} 7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end{array}\right]$

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