Consider a system of n linear equations in n unknowns,

Chapter 5, Problem 41

(choose chapter or problem)

Consider a system of n linear equations in n unknowns, such as the one from Example 63: x + y = 70 24x + 14y = 1180 If a = c 1 1 24 14d X = c x y d b = c 70 1180d then the system of equations can be represented in matrix form by a # X = b If A, the matrix of coefficients, is invertible, then we can multiply both sides of the above equation by a1 , giving a1 # (a # X) = a1 # b (a1 # a) # X = a1 # b (matrix multiplication is associative) i # X = a1 # b (definition of a1 ) X = a1 # b (definition of I) Therefore the solution to the system of equations is given by X = a1 # b Make use of Exercise 39 to find a1 , and use this approach to solve the system of equations.