Write v as a linear combination of u1 u2 and u3 if possible

Write v as a linear combination of u1, u2, and u3, if possible. (Enter your answer in terms of u1, u2, and u3. If not possible, enter IMPOSSIBLE.)

Solution

A linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results

v=au₁+bu₂+cu_{3 ................................................................}(1)

here given that

v=(-1,7,2), u₁=(3,2,8), u₂=(1,-3,-1), u₃=(-2,1,-3)

(-1,7,2)=a(3,2,8)+b(1,-3,-1)+c(-2,1,-3)

(-1,7,2)=(3a+b-2c,2a-3b+c,8a-b-3c)

3a+b-2c=-1..............................................(2)

2a-3b+c=7 .................................................(3)

8a-b-3c=2 ....................................................(4)

solving equation 2,3,and 4,we will get

a=

b=

c=

**NOTE:NOT POSSIBLE TO FIND value a,b,c

so linear combination of u_1, u_2,and u₃ is IMPOSSIBLE