Question

Write v as a linear combination of u1, u2, and u3, if possible. (If not possible, enter IMPOSSIBLE.) v = (7, −14, −3, −4), u1 = (2, −3, 2, 2), u2 = (−3, 2, 1, 2), u3 = (0, −1, −1, −1)

Answer 1

Answer:

IMPOSSIBLE

Step-by-step explanation:

Answer 2

The relation v = 5u₁ + u₂ + u₃ is not followed by the third and fourth coordinates then the linear combination is impossible.

What is a function?

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The v is a linear combination of u₁, u₂, and u₃.

v = (7, −14, −3, −4), u₁ = (2, −3, 2, 2), u₂ = (−3, 2, 1, 2), u₃ = (0, −1, −1, −1)

Let the relation is given as

v = 5u₁ + u₂ + u₃

Then for the first one

7 = 10 −3 + 0

7 = 7

For the second one

−14 = −15 + 2 −1

−14 = −14

Then for the third one

−3 = 10 + 1 −1

−3 ≠ 10

The linear combination is impossible.

More about the function link is given below.

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