Define the linear transformation T by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T). 8 9 A = (a) ker(T) STEP 1: The kernel of T is given by the solution to the equation T(x) = 0. Let x...

Extracted text: Define the linear transformation T by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T). 8 9 A = (a) ker(T) STEP 1: The kernel of T is given by the solution to the equation T(x) = 0. Let x (x1, X2, X3) and find x such that T(x) = 0. (If there are an infinite number of solutions use t and s as your parameters.) || %3D X = STEP 2: Use your result from Step 1 to find the kernel of T. (If there are an infinite number of solutions use t and s as your parameters.) ker(T) :s, : (b) nullity(T) STEP 3: Use the fact that nullity(T) = dim(ker(T)) to compute nullity(T). (c) range(T) STEP 4: Transpose A and find its equivalent reduced row-echelon form. 8 8. 4 9. AT = STEP 5: Use your result from Step 4 to find the range of T. O {(t, -t, - : t is real 2 O R2 R O {(t, -t, t): t is real} o {(t, t, -t, t : t is real (d) rank(T) STEP 6: Use the fact that rank(T) = dim(range(T)) to compute rank(T). o lo o lo + |