call inv

[Bal23]

b={4 9, 16 25, 36 49}; x={7 5, 16 9}; a=sqrt(b); * Assign square root of each element of B to corresponding element of A; y=inv(x); * Call INV function to compute inverse matrix of X and assign results to Y; r=rank(x); I do not know how inv is calculated. I do not know how I can get the follow numbers. Can you explain the function of inv?Thanks. -0.529412	0.2941176
0.9411765	-0.411765

[Rick_SAS]

If Y is the inverse matrix of X, then Y*X = I, where I is the identity matrix that has 1s on the diagonal and 0s off the diagonal.

The inverse matrix is used to solve matrix equation. For example, if you are given a square nxn matrix A and and an nx1 vector w, then you might want to know if there is a vector v such that 

A*v = w

Under certain conditions, the solution is the vector v = inv(A)*w.

[Bal23]

Thanks. I am not clear for some parts. Why I get negative numbers for inv?

[Rick_SAS · Accepted solution]

Because the negative values are required so that X*inv(X) = I.

Since your example is a 2x2 matrix, there is even a formula for the inverse.  for any numbers a,b,c, and d, define the matrix 

A = {a b, c d};

Then 

inv(A) = {d -b, -c a} / (ad-bc);

So you can see that if all the original elements are positive, then exactly two of the elements in the inverse must be negative.