Use matrix inverses to solve systems

What you'll learn

1. Explain what it means for a 2x2 matrix to have an inverse: A^-^1 such that AA^-^1 = A^-^1A = I
2. Compute the inverse of a 2x2 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 3x3 and larger matrices

Prerequisites

• Represent systems as matrix equations