Inverses & Systems

Solving equations with matrices

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A system of equations is $A\mathbf x = \mathbf b$, solved by $\mathbf x = A^{-1}\mathbf b$.
• $2 \times 2$ inverse: swap $a$ and $d$, negate $b$ and $c$, divide by $ad - bc$.
• $\det A = 0$ means no inverse, and either no solution or infinitely many.

Steps

1. Two lines
2. The same system as a matrix
3. Compute an inverse
4. When there is no inverse
5. Solve a system
6. Find the bad value