# Thread: prove linear independent

1. ## prove linear independent

Let U and W be orthogonal subspaces
1) prove that U $\bigcap$ W = {0}
2) if { $u_1,u_2,....u_m$ }is a linearly independent subset of U and { $w_1,w_2,...w_n$}is a linearly independent subset of W, prove that { $u_1,u_2,....,u_m, w_1,w_2,...,w_n$} is a linearly independent set in V.

2. Originally Posted by wopashui
Let U and W be orthogonal subspaces
1) prove that U $\bigcap$ W = {0}
2) if { $u_1,u_2,....u_m$ }is a linearly independent subset of U and { $w_1,w_2,...w_n$}is a linearly independent subset of W, prove that { $u_1,u_2,....,u_m, w_1,w_2,...,w_n$} is a linearly independent set in V.

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Tonio