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Back to Use matrix inverses to solve systems — Problem 5 · 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

1.

Use A−1=[2−1−53]A^{-1} = \begin{bmatrix} 2 & -1 \\ -5 & 3 \end{bmatrix} to solve the system 3x+y=113x + y = 11 and 5x+2y=195x + 2y = 19. Show the matrix multiplication x=A−1b\mathbf{x} = A^{-1}\mathbf{b}.