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

Work through problems with immediate feedback

Recall / Warm-Up

Which of the following matrices does NOT have an inverse?

Every square matrix has an inverse.

$\begin{bmatrix} 3 & 1 \\ 5 & 2 \end{bmatrix}$ — because the determinant is $6 - 5 = 1 \neq 0$

$\begin{bmatrix} 4 & 2 \\ 6 & 3 \end{bmatrix}$ — because the determinant is $12 - 12 = 0$

$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ — because the identity matrix has no inverse