From 73a7ba3edd79df066f2825fc7c1daaa926c8eb9a Mon Sep 17 00:00:00 2001
From: drbsantos <drbsantos@bportugal.pt>
Date: Thu, 14 May 2026 15:21:05 +0100
Subject: [PATCH] Update cachematrix.R

---
 cachematrix.R | 27 ++++++++++++++++++++++++++-
 1 file changed, 26 insertions(+), 1 deletion(-)

diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..863aa7b01db 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -2,14 +2,39 @@
 ## functions do
 
 ## Write a short comment describing this function
+        ##The first function, `makeCacheMatrix` creates a special "Matrix", object that can cache its inverse.
 
-makeCacheMatrix <- function(x = matrix()) {
 
+makeCacheMatrix <- function(x = matrix()) {
+ inv<- NULL
+    set <- function(y){
+        x <<- y
+        inv <<- NULL
+    }
+    
+    get<- function() x
+    setinv <- function(inverse) inv <<- inverse
+    getinv <- function() inv
+    list(set= set, get=get,
+         setinv = setinv,
+         getinv = getinv)
 }
 
 
 ## Write a short comment describing this function
+        ##This second function computes the inverse of the special "matrix" (obtained bu solve function) returned by `makeCacheMatrix` above. 
+        ##If the inverse has already been calculated (and the matrix has not changed), then`cacheSolve` should 
+        ##retrieve the inverse from the cache.
 
 cacheSolve <- function(x, ...) {
         ## Return a matrix that is the inverse of 'x'
+         inv <- x$getinv()
+    if(!is.null(inv)){
+        message("getting cached data")
+        return(inv)
+    }
+    data <- x$get()
+    inv <- solve(data, ...)
+    x$setinv(inv)
+    inv
 }