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Question

The vector  is one of the vectors that are linearly dependent with the vector 2^i+3^j
  1. ^i+^j
  2. 4^i^j
  3. 4^i+6^j


Solution

The correct option is C 4^i+6^j
The given vector is 2^i+3^j

Let it be a

If a and b are linearly dependent, then
xa+yb=0 where x and y are not simultaneously zero.

Now, among the given vectors, let's consider 4^i+6^j

If it is linearly dependent with 2^i+3^j, then

x(2^i+3^j)+y(4^i+6^j)=0 When x and y are not simultaneously 0

When x = 2 and y = -1, x(2^i+3^j)+y(4^i+6^j)=0

Thus, 4^i+6^j is linearly dependent with 2^i+3^j

 

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