Consider the set 8 4 4 8 in R2 Why isnt the set a basis for

Consider the set {(-8, -4), (-4, -8)} in R^2| Why isn\'t the set a basis for R^2? (check all that apply) The vectors are linearly dependent The span of the vectors is not R^2 None of the above, it is a basis for R^2| Online Math Lab resources for this problem: Linear Combinations and Span Linear Independence Bases

Solution

Let, a,b so that

a(-8,-4)+b(-4,-8)=0

-8a-4b=0

-4a-8b=0

b=-2a,

a=-2b

So, b=4b

Hence, a=b=0

So the given two vectors are linearly independent

Hence they form basis for R2

C. none of the above