Linear Algebra help

[Guest]

Studying for finals, not sure about serveral sample problems, please help, very important!

prove det(cA) = c^ndet(A)
(hint: write cA = cIA and use a property of determinants)


True False
c.) If A is row-equivalent to I, and B is row equivalent to C, then AB is row equivalent to C.
d.) If A is not row equivalent to I, then the system of equation Ac = b has infinitely many solutions for any choice of b
e.) If the system of equation Ax =b has no solutions, then A is not row-equivalent to I

 

[galactus]

Since a common factor of any row can be moved through the determinant

sign, and since each of the n rows in cA has a common factor c, we get:

\(\displaystyle det(cA)=c^{n}det(A)\)