Determine whether the transformation is one-to-one and/or onto. PROVE YOUR ANSWER. 3. Let 7: R4 → R³ be defined by T(x) = Ax, where A is the following matrix: 1-20 0 -30-11 0-6-11

Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.

Consider the matrices below. X=[1201],Y=[1032],Z=[3412],W=[3241] Find scalars a,b, and c such that W=aX+bY+cZ. Show that there do not exist scalars a and b such that Z=aX+bY. Show that if aX+bY+cZ=0, then a=b=c=0.

1. Let Ta : ℝ2 → ℝ2 be the matrix transformation corresponding to . Find , where and .