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Problem 166

Find the inverse of A where $$ \mathrm{A}=\mid \begin{array}{rr} 2 & 3 \mid \\ \mid 3 & 5 \mid \end{array} $$

Expert verified

The inverse of matrix A is:
$$
\mathrm{A}^{-1}=\mid \begin{array}{rr}
5 & -3 \mid \\\
\mid -3 & 2 \mid
\end{array}
$$

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Chapter 6

Find the inverse of A where $$ \mathrm{A}=\begin{array}{rrr} 1 & 2 & -1 \\ 2 & 5 & 4 \\ \mid 3 & 7 & 4 \end{array} $$

Chapter 6

Show that \(\mathrm{A}\) is not invertible where $$ \mathrm{A}=\begin{array}{llr} 1 & 6 & 4 \\ 2 & 4 & -1 \\ -1 & 2 & 5 \end{array} \mid $$

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 $$ \mathrm{A}=\begin{array}{ccc} 1 & 2 & 3 \\ 2 & 5 & 3 \\ 1 & 0 & 8 \end{array} $$

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) $\quad \begin{array}{rrr} & \mid 3 & 1 & 0 \\ & A=\mid 1 & -1 & 2 \mid \\\ & \mid 1 & 1 & 1 \mid\end{array}$

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