- #1
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- 786
Suppose the vectors ##v_a## and ##v_b## are linearly independent, another vector ##v_c## is linearly dependent to both ##v_a## and ##v_b##. Now if I form a new vector ##v_d##, where ##v_d = v_b+cv_c## with ##c## a constant, will ##v_d## be linearly independent to ##v_a##?
I need to check how I can satisfy the equation
$$C_1 v_a + C_2 v_d = 0$$
If that's only possible when ##C_1 = C_2 = 0##, then ##v_a## and ##v_d## are linearly independent, but I don't think that's necessarily the case.
I need to check how I can satisfy the equation
$$C_1 v_a + C_2 v_d = 0$$
If that's only possible when ##C_1 = C_2 = 0##, then ##v_a## and ##v_d## are linearly independent, but I don't think that's necessarily the case.