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HSA.REI.C.9 Tutor Intake — Matrix Inverses

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Grade 9·8 problems·~13 min·Common Core Math - HS Algebra·standard·hsa-rei-c-9
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A

Procedures

1.

Using the formula A−1=1det⁡(A)[d−b−ca]A^{-1} = \frac{1}{\det(A)}\begin{bmatrix}d & -b\\-c & a\end{bmatrix},
find A−1A^{-1} for A=[3121]A = \begin{bmatrix}3 & 1\\2 & 1\end{bmatrix}
(where det⁡(A)=1\det(A) = 1).

A^{-1} = \begin{bmatrix}   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   &   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   $\  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   &  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   \end{bmatrix}$

r1c1:
r1c2:
r2c1:
r2c2: