- #1
Yankel
- 395
- 0
Hello all, I have a matrix A:
\[\begin{pmatrix} 2 &4 &1 \\ -4 &7 &3 \\ 5 &1 &-2 \end{pmatrix}\]
and I need to find the adjoint of the matrix inverse.
I found adj(A) to be:
\[\begin{pmatrix} -17 &9 &5 \\ 7 &-9 &-10 \\ -39 &18 &30 \end{pmatrix}\]
and I found the determinant of A to be -45 and the determinant of adj(A) to be 2025.
Now based on:
\[adj(A^{-1})=(adj(A))^{-1}\]
I tried solving the question, I did:
\[B=adj(A))\]
and looked for:
\[B^{-1}\]
This way:
\[B^{-1}=\frac{1}{\left | B \right |}adj(B)\]
and got:
\[\frac{1}{2025}A\]
which is not the answer. the answer should be:
\[-\frac{1}{45}A\]
And I don't understand what I did wrong here.
Thank you
\[\begin{pmatrix} 2 &4 &1 \\ -4 &7 &3 \\ 5 &1 &-2 \end{pmatrix}\]
and I need to find the adjoint of the matrix inverse.
I found adj(A) to be:
\[\begin{pmatrix} -17 &9 &5 \\ 7 &-9 &-10 \\ -39 &18 &30 \end{pmatrix}\]
and I found the determinant of A to be -45 and the determinant of adj(A) to be 2025.
Now based on:
\[adj(A^{-1})=(adj(A))^{-1}\]
I tried solving the question, I did:
\[B=adj(A))\]
and looked for:
\[B^{-1}\]
This way:
\[B^{-1}=\frac{1}{\left | B \right |}adj(B)\]
and got:
\[\frac{1}{2025}A\]
which is not the answer. the answer should be:
\[-\frac{1}{45}A\]
And I don't understand what I did wrong here.
Thank you