Question

in a linear transform, when the orientation of space is inverted, the determinant value is negative. true or false

Answer 1

In linear transformation we use determinant to determine the orientation of the space.  This we do by considering the sign before the determinant.  If the determinant is positive then the Transformation reserves the orientation.  However if the determinant is negative, the Transformation reverses or rather inverts the orientation.   We can now answer the question above confidently from the given explanation.   The answer is thus :  TRUE.