Which of the following sets of vectors are linearly independent? [-8 -9 -4] , [7

Question

Which of the following sets of vectors are linearly independent? [-8 -9 -4] , [7 8 -6] , [1 1 10] [-4 7] , [8 -6] , [9 3] [5 -2] [0 0] , [-8 6] [-18 -6] , [-9 -3]

Explanation / Answer

A)-8x+7y+z = 0 -9x+8y+z = 0 => z = 9x-8y -4x-6y+10z = 0 =>-8x+7y+9x-8y = 0 =>x-y = 0 =>x = y =>z = 9x-8x = x So not linearly independent. B)-4x+8y+9z = 0 7x-6y+3z = 0 So two equations and three unknowns So not linearly independent. C)There is not set of vectors as there is only one vector. So Option C is wrong. D)-8x = 0 => x = 0 6y = 0 => y = 0 Linearly Independent.....Option D is correct E)Not linearly independent.

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