বিপরীত ম্যাট্রিক্স
If A=[−1−2−221−22−21]A = \begin{bmatrix}-1 & -2 & -2 \\ 2 & 1 & -2 \\ 2 & -2 & 1\end{bmatrix}A=−122−21−2−2−21, Then adj(A)adj(A)adj(A) equals
AAA
ATA^TAT
3A3A3A
3AT3A^T3AT
Given A=[−1−2−221−22−21]A = \begin{bmatrix}-1 & -2 & -2 \\ 2 & 1 & -2 \\ 2 & -2 & 1\end{bmatrix}A=−122−21−2−2−21
AT=[−122−21−2−2−21]A^{T}=\begin{bmatrix} -1 & 2 & 2 \\ -2 & 1 & -2 \\ -2 & -2 & 1 \end{bmatrix}AT=−1−2−221−22−21
Now, adjA=CT=[−3−6−663−66−63]Tadj A=C^{T}={\begin{bmatrix} -3 & -6 & -6 \\ 6 & 3 & -6 \\ 6 & -6 & 3 \end{bmatrix}}^{T}adjA=CT=−366−63−6−6−63T
⇒adjA=[−366−63−6−6−63]\Rightarrow adj A=\begin{bmatrix} -3 & 6 & 6 \\ -6 & 3 & -6 \\ -6 & -6 & 3 \end{bmatrix}⇒adjA=−3−6−663−66−63
⇒adjA=3[−122−21−2−2−21]\Rightarrow adj A=3\begin{bmatrix} -1 & 2 & 2 \\ -2 & 1 & -2 \\ -2 & -2 & 1 \end{bmatrix}⇒adjA=3−1−2−221−22−21
⇒adjA=3AT\Rightarrow adj A=3A^{T}⇒adjA=3AT
যদি B= [201−2] \left [ \begin{matrix} 2 & 0 \\ 1 & - 2 \end{matrix} \right ] [210−2] হয় তবে, B−1 B^{- 1} B−1 নিচের কোনটি?
A=[7x210],B=[56−7−9] A = \left [ \begin{matrix} 7 & x \\ 2 & 10 \end{matrix} \right ] , B = \left [ \begin{matrix} 5 & 6 \\ - 7 & - 9 \end{matrix} \right ] A=[72x10],B=[5−76−9]
B-1 = ?
For square matrices AAA and BBB of the same order, we have adj(AB)=?adj (AB) = ?adj(AB)=?
A একটি 4×4 ম্যাট্রিক্স |A|=64 হলে, ∣A2∣−1 \left \lvert \frac{A}{2} \right \rvert^{- 1} 2A−1 =?
