Linear combinations, span, subspaces, linear dependence

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Vectors are written as rows in these questions. R^n is the real vector space with n coordinates. Enter your answer as concisely as possible.

Find 'b' such that span((1,2), (4,b)) is not the entire plane.

1 point

Two vectors in R^2 are linearly dependent if and only if they both lie on the same line through the origin.

1 point

True

False

Clear selection

Find 'a' and 'b' such that (2,6) = a (1,2) + b (2,3). Write answer as a,b. Do not type any spaces.

3 points

Find 'b' such that (1,2,3), (3,4,5) and (2,6,b) are linearly dependent.

2 points

Suppose 'a' and 'b' are such that (1,2,3), (2,3,4) and (2,a,b) are linearly dependent. Find 2020a-1010b.

3 points

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