Back to Use matrix inverses to solve systems — Problem 2 · Task Set 48

Exercises: Find Matrix Inverses and Solve Systems

For all inverse computations, verify your result by checking that AA⁻¹ = I. For system solutions, verify by substituting into the original equations.

Grade 11·18 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-rei-c-9

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Fluency Practice

$A diagram showing a 2x2 matrix [a,b;c,d] with three labeled steps: Step 1 Swap a and d, Step 2 Negate b and c, Step 3 Divide by det(A) = ad minus bc.$

Use the 2×2 inverse formula to find $A^{-1}$ for $A = \begin{bmatrix} 3 & 1 \\ 5 & 2 \end{bmatrix}$ .

Steps: (1) compute $\det(A)$ , (2) apply the formula $A^{-1} = \frac{1}{\det(A)}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$ , (3) verify $AA^{-1} = I$ .