Help with exercise 6 please? Exercise 6Is the set of vectorsV = {r² + 2t – 1,3t + 5, –t² + t + 6}linearly dependent?Example 6What about this set of vectors?O = {t² + 2t + 1, t? - t +3,3t +1}Is it linearly dependent? Let's check. First, set it as a linear combination of the vectors set equal to the zero vector, .a (t? + 2t + 1) +b(t? - t+3) + c(3t + 1) =(a + b)t? + (2a – b+3c)t + (a + 3b +c)= 0Again, make sure you see how this works algebraically. This yields the following system of equations, augmented matrix and resultingRREF matrix.a +6 = 02a - b+ 3c =a + 36 +c =10: 01 0 0: 0RREF,2-1 3: 00 10: 01310 0 1Remember from previous tutorials that this means that this system only has one solution. That solution is (a, b, c) = (0,0,0). Thisis the trivial solution! Because this is the only solution, we do NOT say that the set of vectors 0 is linearly dependent. In fact,was say that the set of vectors O is linearly independent. Going back to the top of the tutorial, this also means that none ofthe vectors in 0 can be written as a linearly combination of the others. That makes them independent, yes? They cannot bewritten as a linear combination of the others. Or, they are not defined by the other vectors. They are their own vector. Alone.Independent!What you should notice about all of these Examples and Exercises is that when you do the row-reduction procedure the rightcolumn stays full of zeros. It's always just zeros. For that reason you can almost entirely ignore it. Then, the matter of lineardependence boils down to what the A part of the matrix reduces to. Just check the solutions. Is it just all zeros? LinearlyIndependent. Is it anything other than all zeros? Li nearly Dependent.

Name: Help with exercise 6 please? Exercise 6Is the set of vectorsV = {r² +
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Help with exercise 6 please? Exercise 6Is the set of vectorsV = {r² + 2t – 1,3t + 5, –t² + t + 6}linearly dependent?Example 6What about this set of vectors?O = {t² + 2t + 1, t? - t +3,3t +1}Is it linearly dependent? Let's check. First, set it as a li

Question

Accepted Answer

Answered: Image /qna-images/answer/cfbff989-64f3-4545-b97b-74ef820e72d9.jpg

Exercise 6 Is the set of vectors V = {i² + 2t – 1,3t + 5, -t² + t + 6} linearly dependent?