Question #38a9a

1 Answer
Ratnaker Mehta
Nov 19, 2017

# T(x)=[(3x_1+3x_2-3x_3),(-4x_1+x_3)].#

Explanation:

#T(x)=T(x_1e_1+x_2e_2+x_3e_3),#

#=x_1T(e_1)+x_2T(e_2)+x_3T(e_3)........[because, T" is linear],"#

#=x_1[(3),(-4)]+x_2[(3),(0)]+x_3[(-3),(1)]............[because," Given],"#

#=[(3x_1),(-4x_1)]+[(3x_2),(0x_2)]+[(-3x_3),(1x_3)],#

#=[(3x_1+3x_2-3x_3),(-4x_1+0+x_3)],#

# rArr T(x)=[(3x_1+3x_2-3x_3),(-4x_1+x_3)].#

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