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Exercise 16

Avg difficulty 2.5

Find the inverse (if it exists) of each of the matrices AA in Finding Inverses. that is, find the matrix A−1A^{-1} such that AA−1=A−1A=IA A^{-1} = A^{-1} A = I, where I=(1001).I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}.

A=(3−7−25)\displaystyle A = \begin{pmatrix} 3 & -7 \\ -2 & 5 \end{pmatrix}

Judson, The ODE Project, §3.1 Linear Algebra in a Nutshell, Exercise 16

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Adapted from The ODE Project © 2019–2025 Thomas W. Judson. Licensed under CC BY 4.0. Source: The ODE Project. Imported at revision 7935458.