1 point Consider the subset W of R3 consisting of all vector

(1 point) Consider the subset W of R3 consisting of all vectors y such that x +y+z2-2. 2 Select all statements that are correct: A. W is closed under addition. B. W is closed under scalar multiplication. C. There exists a 3 x 3 matrix A whose kernel is W D. W contains the zero vector. E. There exists a 3 X 3 matrix B whose image is W F W is a subspace of R

Solution

A. It is not closed under addition

Consider two points

(0,0,-2) and (0,0,-1) both lie in W

Adding the two points gives

(0,0,-3) which is not in W\\

B. False

(0,0,3) is a point in W

Multiplying by -1 gives

(0,0,-3) which is not in W

C. False

Kernel equation will be an equality not an inequality

D. True

0+0+0=0>-2

E. False

Image set of a matrix will be defined by an equality not an inequalty

F. False

W is not closed under addition or scalar multiplication

Hence not a subspace