Join the IDNLearn.com community and get your questions answered by knowledgeable individuals. Our Q&A platform offers reliable and thorough answers to help you make informed decisions quickly and easily.
Sagot :
To find the inverse of the matrix
[tex]\[ \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 1 & 0 & 1 \end{pmatrix}, \][/tex]
we can follow these steps:
1. Determine the determinant of the matrix: This is essential as it's a requirement for the matrix to be invertible. The determinant must be non-zero.
2. Find the matrix of minors: Calculate the determinant of the 2x2 minor matrices for each element in the original matrix.
3. Find the matrix of cofactors: Apply a checkerboard pattern of plus and minus signs to the matrix of minors.
4. Transpose the matrix of cofactors: This forms the adjugate (or adjoint) of the matrix.
5. Divide each element by the determinant: This will yield the inverse of the original matrix.
However, I will directly provide you with the result obtained from the inverse calculation:
The inverse of the matrix
[tex]\[ \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 1 & 0 & 1 \end{pmatrix} \][/tex]
is
[tex]\[ \begin{pmatrix} 0.5 & -0.5 & 0.5 \\ 1 & 0 & -1 \\ -0.5 & 0.5 & 0.5 \end{pmatrix}. \][/tex]
[tex]\[ \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 1 & 0 & 1 \end{pmatrix}, \][/tex]
we can follow these steps:
1. Determine the determinant of the matrix: This is essential as it's a requirement for the matrix to be invertible. The determinant must be non-zero.
2. Find the matrix of minors: Calculate the determinant of the 2x2 minor matrices for each element in the original matrix.
3. Find the matrix of cofactors: Apply a checkerboard pattern of plus and minus signs to the matrix of minors.
4. Transpose the matrix of cofactors: This forms the adjugate (or adjoint) of the matrix.
5. Divide each element by the determinant: This will yield the inverse of the original matrix.
However, I will directly provide you with the result obtained from the inverse calculation:
The inverse of the matrix
[tex]\[ \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 1 & 0 & 1 \end{pmatrix} \][/tex]
is
[tex]\[ \begin{pmatrix} 0.5 & -0.5 & 0.5 \\ 1 & 0 & -1 \\ -0.5 & 0.5 & 0.5 \end{pmatrix}. \][/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.