Given the vectors u1 = (2, −1, 3) and u2 = (1, 2, 2) find a...

Given the vectors u1 = (2, −1, 3) and u2 = (1, 2, 2) find a third vector u3 in R3 such that

(a) {u1, u2, u3} spans R3
(b) {u1, u2, u3} does not span R3

Solutions

Expert Solution

Here two vectors u1,and u2 are given and we have to find u3 such that in (a) the set {u1,u2,u3} spans R3. For this u3 must be linear independent of both u1 and u2 because the dimension of R3 is equal to 3 so the spanning set must be three elements which are linearly independent.

In(b) the set {u1,u2,u3} does not span R3.For this u3 must be linear dependent .so u3 is a linear combination of u1 and u2.

The complete solution is given below

Colby Messinger answered 1 year ago

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