Write v as a linear combination of u1,U2, and u3, if possible. (Enteryour answer in terms of u1,U2, and u3. If not possible enter IMPOSSIBLE.)v=(−1,7,2),u1(3,2,8),u2(2,−3,1),u3(−2,3,−1)v=_____

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PietAppeteoth22m · Accepted Answer

Step 1Since v is a lianer combination of u1,u2 and u3,sov=c1u1+c2u2+c3u3c1(3,2,8)+c2(2,−3,1)+c3(−2,3,1)=v[32−22−33811][c1c2c3]=[−172]AC=VStep 3So augmented matrix is [A:V],[32−2:−12−33:7811:2]Reduce the above augmented matrixinto raw echelon form,[32−2:−12−33:7811:2]Apply R1→R1→R2−[15−5:−82−33:7811:2]Apply R2→R2−2R1.R3→R3−8R1−[15−5:−80−1313:230−3939:66]Apply R3→R3−3R2−[15−5:−80−1313:23000:−3]Here rank of a matrix A=2Rank of matrix [A:B]=3So rank of (A)≠ rank of (A:B)That is system is consistentStep 3Hence Since v is not a linear combination of u1,u2 and u3

Write v as a linear combination of u_{1}, U_{2}, and

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