Let #\mathcal{B} = {[[-2],[-1]][[3],[4]]} = {vecv_1, vecv_2}# find #[vecx]_\mathcal{E} # Knowing that #[vecx]_\mathcal{B}= [[-5],[3]]#?

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Answer 1 · 2018-07-06T18:16:31

# (19,17)#.

#vecx# has been represented as #(-5,3)# using the basis vectors

#vecv_1=(-2,-1) and vecv_2=(3,4)#.

Hence, using the usual standard basis,

#vecx=-5vecv_1+3vecv_2#,

#=-5(-2,-1)+3(3,4)#,

#=(10,5)+(9,12)#,

#=(19,17)#.