Invertible Matrix Theorem

Invertible Matrix Theorem : Let A be an nxn matrix. Then the following statements are equivalent. That is, for given A, the statements are either all true or all false.

1st Term: a : A is an invertible matrix

f : The linear transformation x -->Ax

g : The equation Ax=b has at least one solution for each b in R^n

l : A^T(transpose) is an invertible matrix

m : The columns of A form a basis of R^n

r : dimNulA=0

s : The number 0is not an Eigenvalue of A