For the matrix A given below find a set of vectors {V₁,..., Vk} such that Nul (A) Span (V₁,..., Vk). -8 4 -3] -3 -3 A -2 -1 -4 0 0 1 1

Let A = A3x3 have column vectors of aj, a2, a2 be such that a1 + 2a2 = 3a3. Which of the following vectors is in N(A)? 1 3 1 2 -3 -3 1 -3/2 1

The set of vectors {(1,1,0,0),(0,-1,0,0),(0,0,1,1),(1,0,1,1)} is linearly dependent. What is a valid expression of the last vector as a linear combination of the others? a. (1,0,1,1)=(1,1,0,0)+(0,-1,0,0)-(0,0,1,1) b. (1,0,1,1)=(1,1,0,0)+(0,-1,0,0)+(0,0,1,1) c. (1,0,1,1)=-(1,1,0,0)+(0,-1,0,0)+(0,0,1,1) d. (1,0,1,1)=2(1,1,0,0)+2(0,-1,0,0)+2(0,0,1,1)

Let v,=( 2, 5, 3 ), v2 = ( 1, 1, 1 ) and v3 = (4 , -2, 0 ) are vectors in R3 then are .a Linear independent .b Linear dependent