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

Fluency Practice

For which matrix does an inverse NOT exist?

$\begin{bmatrix} 5 & 2 \\ 3 & 1 \end{bmatrix}$ , because $\det = 5 - 6 = -1$

$\begin{bmatrix} 1 & 2 \\ 3 & 6 \end{bmatrix}$ , because $\det = 6 - 6 = 0$

$\begin{bmatrix} 7 & 0 \\ 0 & 3 \end{bmatrix}$ , because it is a diagonal matrix

$\begin{bmatrix} -2 & 4 \\ 1 & -1 \end{bmatrix}$ , because it has negative entries