Question

linear algebra: show all work please

ned by Xi = I Find a basis 4. Let S be the subspace of R4 spanned b (1,0, 2, 1)? and x2 = (0, 1, 3, -2)7. Find for St.

Answer 1

(1) Its given that s is the subespace of RA spanned by ?4 ( 190 ) -2; 137 and 32= (0,113, -3)? Now st={VERA : <uut=0 for every ues} . Let v= (149 22 i 23, 2) be an element in st. Then <ü, xxx.=0 and <; az>= 0 ... 1.to.^2 - 2199+xy=0. and ornit1.02 +3.23-2a4=0 Let a 24 - 213 +21=0 .. and. x2 +3a3-2xy =0 dz=a, 24=b. Then su = * 223-24 ; = 29-b and az = 2x4-323 ... = 2b3a : so Calma, as, ku) = (22-b, 26-3a; 207.b) 30(2,-3, 1,0) ++b(-1,2,0,1) Therefore st = span {(2, -3,1,0) 7 (-1,210,17%}

(2,-3, 1,0) and (0; 2;0, 1T are not a scator multiple of each other. so they are linearly independenti Hence {(2,-314,0), (4;2:00"} ssa basis for sta