I am trying to construct a Zero Coupon Yield curve for US Government Bonds from market data (coupons, face values, prices, months to maturity) via Bootstrapping. However, I am not too sure how I would go about solving the equation AP = F over here if I have the Matrix A such that it isn't square. I currently have more columns (which represent the months between each coupon payment) than rows (each row represents a bond with a particular number of months to maturity). For example one of the bonds I have has a coupon issued every 3 months and the maximum months to maturity among the bonds is 360, which implies my matrix A has 120 columns. However, I have only 60 rows as I have only 60 bonds with unique months to maturity, leaving matrix A as non-square. I am sure this is easily solvable but I haven't been able to find anything on this.
Thank You