Determine if the given vector is in the range of t(x) = ax where a = [1 -2 0 3 2 1] y = [-3 6] y = [1 -4] y = [2 7] Suppose that a linear transformation T satisfies

## Answer

Soin Since T(x) = AX Let oc=ari 2 ag then Tx)=AX= 1 -2 all 3 xg X3 ( x 1-2×2 3×1 +222 +23 Now, 5 Take x =- 19 X2 = 1 and x₃=7 -3 then T(X)= Ax=1-1-2 -3+2+7 +7 6 – B [3] is in the range of T(x)=AX . 6 Take x = -lang= -1 and x3=1 then T(X) = AX= -l+g -3-2+1 -4 .]=(- [A] is in the is in the range of T(X= AX.

Take 2,20 979 = -1 and lz=9 then Tx)= AX = Ota 2 2 -2 +9 [ ㅋ 7 [i] is in the range og TUI) = AX Take x1=0 a X=-2 and X₂=9 9 then T(X)= Ax= 4 – 4+9 5 = [5] 1 & [ 4 ] is in the range of TX)= Ax.