Writing a Linear Combination In Exercises 5 3 and 5 4 , use a software program or a graphing utility to write v as a linear combination of u 1 , u 2 , u 3 , u 4 , and u 5 . Then verify your solution. v = ( 5 , 8 , 7 , − 2 , 4 ) u 1 = ( 1 , 1 , − 1 , 2 , 1 ) u 2 = ( 2 , 1 , 2 , − 1 , 1 ) u 3 = ( 1 , 2 , 0 , 1 , 2 ) u 4 = ( 0 , 2 , 0 , 1 , − 4 ) u 5 = ( 1 , 1 , 2 , − 1 , 2 )
Writing a Linear Combination In Exercises 5 3 and 5 4 , use a software program or a graphing utility to write v as a linear combination of u 1 , u 2 , u 3 , u 4 , and u 5 . Then verify your solution. v = ( 5 , 8 , 7 , − 2 , 4 ) u 1 = ( 1 , 1 , − 1 , 2 , 1 ) u 2 = ( 2 , 1 , 2 , − 1 , 1 ) u 3 = ( 1 , 2 , 0 , 1 , 2 ) u 4 = ( 0 , 2 , 0 , 1 , − 4 ) u 5 = ( 1 , 1 , 2 , − 1 , 2 )
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Writing a Linear Combination In Exercises
5
3
and
5
4
, use a software program or a graphing utility to write
v
as a linear combination of
u
1
,
u
2
,
u
3
,
u
4
, and
u
5
. Then verify your solution.
Write v as a linear combination of u and w, if possible, where u = (3, 1) and w = (3,-2). (Enter your answer in terms of u and w. If not possible, enter IMPOSSIBLE.)
v = (6, 1)
v = (u +w)
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Write v as a linear combination of
u1,
u2,
and
u3,
if possible. (If not possible, enter IMPOSSIBLE.)
v = (4, −20, −16, −14), u1 = (1, −2, 1, 1), u2 = (−2, 1, 3, 1), u3 = (0, −3, −3, −3)
Write an equation whose graph consists of the set of points P(x, y, z) that are twice as far from A(0, −1, 1) as from B(1, 2, 0). Describe the geometric figure represented by the equation.
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