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Problem 157

Let $\mathrm{A}=\begin{array}{ccc}\mid 1 & 1 & 1 \mid \\ \mid 0 & 1 & 0 \\\ \mid 0 & 1 & 1\end{array}$ Find the inverse of \(\mathrm{A}\).

Expert verified

The inverse of matrix A is:
A⁻¹ = \[\begin{array}{ccc}\mid 1 & -1 & 1 \mid \\\ \mid 0 & 1 & 0 \\\ \mid 0 & -1 & 0\end{array}\]

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Chapter 6

Use the classical adjoint to find \(\mathrm{A}^{-1}\) where $$ \mathrm{A}=\mid \begin{array}{rrr} 1 & 0 & -1 \mid \\ 0 & 2 & 2 \\ \mid 1 & 1 & -1 \mid \end{array} $$

Chapter 6

Find the inverse of $$ \begin{array}{ll} \mid 1 & 2 \\ \mid 3 & 7 \end{array} \mid $$

Chapter 6

Find the inverses of the following matrices. (1) $\quad \mathrm{A}=\mid \begin{array}{ll}3 & 1 \mid \\ \mid-1 & 6 \mid\end{array}$ (2) $\quad \mathrm{A}=\begin{array}{rrr} & 11 & -7 & -14 \\ & \mid 2 & 1 & -1 \\\ & \mid 1 & 3 & 4\end{array}$ (3) $\quad \begin{array}{rrr} & \mid 3 & 1 & 0 \\ & A=\mid 1 & -1 & 2 \mid \\\ & \mid 1 & 1 & 1 \mid\end{array}$

Chapter 6

Let $\mathrm{A}=\begin{array}{ccc}1 & 2 & 3 \mid \\ \mid 1 & 3 & 2 \\ \mid 1 & 1 & 5\end{array}$ Show how we obtain the inverse of \(A\) by reducing the matrix [A: I] to a matrix of the form \([\mathrm{I}: \mathrm{B}]\).

Chapter 6

Find the inverse of the matrix A where $$ \mathrm{A}=\begin{array}{cccc} 11 & 1 & 1 & 1 \\ 0 & 1 & 1 & 1 \\ & 0 & 0 & 1 & 1 \\ & \mid 0 & 0 & 0 & 1 \end{array} $$ Show that the inverse of a diagonal matrix is obtained by inverting the diagonal entries.

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