Find the value of #lambda# such that the vectors #(1,3,5)#, #(2,-1,3)# and #(4, lambda, 1)# are linearly dependent.?

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Answer 1 · 2017-12-15T21:38:36

#lambda = -7#

They are linearly dependent if their determinant is 0.

#| (1,3,5), (2,-1,3), (4, lambda, 1) | = 0#

I use The Rule of Sarrus to compute #3xx3# determinants:

#| (1,3,5,1,3), (2,-1,3,2,-1), (4, lambda, 1,4, lambda) | = 0#

#1(-1)(1)+3(3)(4)+5(2)(lambda)-5(-1)(4)-1(3)(lambda)-3(2)(1)=0#

#7lambda+49=0#

#lambda = -7#