Question

#23

Step 1

Consider the set

S = {(1,1,1) , (1,2,3) , (1,-1,2)} in R^{3}.

We have to show that the vectors in **S **is linearly dependent and linearly independent.

If the set is linearly dependent, then the we can express one of the vectors in S as a linear combination of other vectors in S and if the only linear combination of vectors in that equals the zero vector is the one which all the coefficients are zero,

Suppose that a_{1}, a_{2} and a_{3} are scalars such that:

Step 2

Equating the corresponding coordinates of the vectors on the left and the right sides of the equation, obtain the following system of linear equation:

Step 3

Isolated **a1** from equation **(1)** and put the value of **a1** in equation **(2)** and **(3)**

Substitute **a1 = -a2 –a3**

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