Answer to Question #109049 in Physics for MS

Question #109049
Determine whether or not u&v are linearly dependent
1] u=(1,2,3,4),v=(4,3,2,1)
2]u=2t^2+4t-6, v=4t^2+8t-6
1
Expert's answer
2020-04-13T10:09:46-0400

1)


A=[14233241]    C14C1C2    [0453102151]A=\begin{bmatrix} 1 & 4 \\ 2 & 3 \\3 & 2 \\ 4 & 1 \end{bmatrix} \implies C_1\to 4C_1-C_2\implies \begin{bmatrix} 0 & 4 \\ 5 & 3 \\10 & 2 \\ 15 & 1 \end{bmatrix}

Thus, u and v are linearly dependent.

2)

 

A=[244866]    C2C22C1    [204066]A=\begin{bmatrix} 2 & 4 \\ 4 & 8 \\-6 & -6 \end{bmatrix} \implies\\ C_2\to C_2-2C_1\implies \begin{bmatrix} 2 & 0 \\ 4 & 0 \\-6 & 6 \\ \end{bmatrix}

Thus, u and v are linearly dependent.


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