For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in C
ID: 2967466 • Letter: F
Question
For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A.
This is matrix A= [8 16]
[-2 -4]
[-6 -12]
[-4 -8]
A nonzero vector in Nul A is _______.
A nonzero vector in Col A is _________.
Explanation / Answer
A= 8 16 -2 -4 -6 -12 -4 -8 WE FIND THAT COL.2 = 2* COL.1 .. SO THEY ARE L.D. SO TAKING COL.1 ONLY 1..NON ZERO VECTOR IN NULL A NULL A IS GIVEN BY A*X = 0 8 16 X 0 -2 -4 * Y = 0 -6 -12 0 -4 -8 0 8X+16Y=0X=-2Y REST ARE ALL DEPENDENT EQNS. SO NULL SPACE IS GIVEN BY ..SAY CHECK A*[V]=0 X= -2 8 16 -2 0 Y= 1 ..ANSWER -2 -4 * 1 = 0 OR..IN GENERAL -2K -6 -12 0 K -4 -8 0 WHERE K IS ANY REAL NUMBER 2..NON ZERO VECTOR IN COL. A WE CAN TAKE COL.1 IT SELF AS ONE NON ZERO VECTOR IN COL A SO THE ANSWER IS 8 -2 -6 -4