Question

linear algebra

Find the coordinate matrix of x in RP relative to the basis B'. B' = {(1, -1, 2, 1), (1, 1, -4,3), (1, 2, 0,3), (1, 2, -2, 0)}, x = (16, 10,-8, 7) [x]B 11

Answer 1

-84 87) x=( 16; 10, B's F64-1,212, 4, 6-4,3), (1,90731,11,2,2,033 B = £ 6.3, Gy.I. b روما x ? d Xabi+ bbgt Cobz+ d by X = al 1,-1,9,11 + bli, -4,3)+((, 2013) 7 dl 112,-0.01 (16,109,-8,7) = ali,-1,2,11 + bc1, 1-4, 3) Tel119,0,31 + d( 1, 2, -2, 0) Now White in Matrin for in 16 1 2 es 10 2 -4 3 O --8 3 Now Convert into Row echlin form Ra R. th, and R₂ har 9 3 3 -4 -6. 3 16 36 40 7. 3

Now operate Ry Rai Ri Rola and Riz Rz-bRq { 16. 3 13 more 3 2 7 38 -9 2 2 Ry Pyg R and R₂ Ral 312 312 517 16 13 3817 -35 O O al -4 Ry and Ry Rz Ry Ryti -23 And R3 → R3 - f RA - 1 16 13 0 312 312 0 १ 0 0 Ro Ro 3 Ry RR - Ry it 1 O i 3/2 -12 o o 9 G

- RR - R Ro - 3 Rz RR - Re and 7 0 1 0 - O a = 7 bal ا- دم d- Hence (16.10, -8,7) = 764,-1,2,1)+1(14-43) -It! 2,013) + 9(1,2,=2,0) Soy [x] = 7 १