5) the equation ax = 5 is consistent, if and only if ū is in the span of columns of matrix a. 6) a linear transformation x + ax is one-to-one if the equation ax = 5 is always consis- tent. 7) a linear transformation x + ax is onto, if columns of matrix a span codomain of the transformation. 8) if the columns of matrix a is linearly independent, then the linear transformation x ax is one-to-one. every non-zero n x n matrix a is invertible. ) if a linear transformation x ax is one-to-one and onto, then the matrix a is invert-