જો A=left[begin{array}{ccc}2 & -1 & 1 -1 & 2 | vedclass

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(A) આપેલ છે $A=\left[\begin{array}{ccc}2 & -1 & 1 \ -1 & 2 & -1 \ 1 & -1 & 2\end{array}ight]$.પ્રથમ,$A^{2} = A 	imes A = \left[\begin{array}{ccc}

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$\frac{1}{4}\left[\begin{array}{ccc}3 & 1 & -1 \ 1 & 3 & 1 \ -1 & 1 & 3\end{array}ight]$

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(A) આપેલ છે $A=\left[\begin{array}{ccc}2 & -1 & 1 \ -1 & 2 & -1 \ 1 & -1 & 2\end{array}ight]$.પ્રથમ,$A^{2} = A 	imes A = \left[\begin{array}{ccc}2 & -1 & 1 \ -1 & 2 & -1 \ 1 & -1 & 2\end{array}ight] \left[\begin{array}{ccc}2 & -1 & 1 \ -1 & 2 & -1 \ 1 & -1 & 2\end{array}ight] = \left[\begin{array}{ccc}6 & -5 & 5 \ -5 & 6 & -5 \ 5 & -5 & 6\end{array}ight]$ શોધો.ત્યારબાદ,$A^{3} = A^{2} 	imes A = \left[\begin{array}{ccc}6 & -5 & 5 \ -5 & 6 & -5 \ 5 & -5 & 6\end{array}ight] \left[\begin{array}{ccc}2 & -1 & 1 \ -1 & 2 & -1 \ 1 & -1 & 2\end{array}ight] = \left[\begin{array}{ccc}22 & -21 & 21 \ -21 & 22 & -21 \ 21 & -21 & 22\end{array}ight]$ શોધો.હવે,$A^{3}-6 A^{2}+9 A-4 I = \left[\begin{array}{ccc}22 & -21 & 21 \ -21 & 22 & -21 \ 21 & -21 & 22\end{array}ight] - 6\left[\begin{array}{ccc}6 & -5 & 5 \ -5 & 6 & -5 \ 5 & -5 & 6\end{array}ight] + 9\left[\begin{array}{ccc}2 & -1 & 1 \ -1 & 2 & -1 \ 1 & -1 & 2\end{array}ight] - 4\left[\begin{array}{ccc}1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1\end{array}ight] = \left[\begin{array}{ccc}0 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & 0\end{array}ight] = 0$ ચકાસો.$A^{-1}$ શોધવા માટે,સમીકરણ $A^{3}-6 A^{2}+9 A-4 I=0$ ને $A^{-1}$ વડે ગુણતા:$A^{2}-6 A+9 I-4 A^{-1}=0 \Rightarrow 4 A^{-1} = A^{2}-6 A+9 I$.$4 A^{-1} = \left[\begin{array}{ccc}6 & -5 & 5 \ -5 & 6 & -5 \ 5 & -5 & 6\end{array}ight] - 6\left[\begin{array}{ccc}2 & -1 & 1 \ -1 & 2 & -1 \ 1 & -1 & 2\end{array}ight] + 9\left[\begin{array}{ccc}1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1\end{array}ight] = \left[\begin{array}{ccc}3 & 1 & -1 \ 1 & 3 & 1 \ -1 & 1 & 3\end{array}ight]$.આમ,$A^{-1} = \frac{1}{4}\left[\begin{array}{ccc}3 & 1 & -1 \ 1 & 3 & 1 \ -1 & 1 & 3\end{array}ight]$.

જો $A=\left[\begin{array}{ccc}2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2\end{array}\right]$ હોય,તો ચકાસો કે $A^{3}-6 A^{2}+9 A-4 I=0$ અને તે પરથી $A^{-1}$ શોધો.

Similar Questions

જો $A = \begin{bmatrix} 3 & 2 \\ 0 & 1 \end{bmatrix}$ હોય,તો $(A^{-1})^3$ ની કિંમત શોધો.

$\begin{aligned} & A(\alpha, \beta)=\left[\begin{array}{ccc}\cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^\beta\end{array}\right] \\ & \Rightarrow[A(\alpha, \beta)]^{-1}=\end{aligned}$

જો $k$ એક અદિશ હોય અને $I$ એ $3$ કક્ષાનો એકમ શ્રેણિક હોય,તો $adj(kI) = $

જો $A = \frac{1}{7} \begin{bmatrix} 3 & -2 & 6 \\ -6 & -3 & 2 \\ -2 & 6 & 3 \end{bmatrix}$ હોય,તો:

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