Use matrix inverses to solve systems

What you'll learn

1. Explain what it means for a 2×2 matrix to have an inverse: A⁻¹ such that AA⁻¹ = A⁻¹A = I
2. Compute the inverse of a 2×2 matrix using the formula A⁻¹ = (1/det(A)) · [d -b; -c a] where A = [a b; c d] and det(A) = ad - bc
3. Determine whether a matrix is invertible by checking whether the determinant is nonzero
4. Use the matrix inverse to solve the system Ax = b: compute x = A⁻¹b
5. Use technology (graphing calculator or software) to find inverses and solve matrix equations for 3×3 and larger matrices

Prerequisites

• Represent systems as matrix equations