4. let b = {(1,0,,1,2), (2, -1,0)}. (a) the vectors in b are dependent. show this. (b) find a non-trivial solution to an(1,0,1) + a2(0,1,2) + a3(2, -1,0) = 0. (c) b is not a basis for the span(b). find a basis for the span span(b).

Step-by-step explanation:

Given are three vectors in set B.

To show that B is dependent

The determinant

Hence vectors are dependent

b) The given equation

Let us try parametrically

These 3 vectors are collinear and hence equation would be

c) Basis for B would be only 2 dimensional

i.e. any two vectors out of 3 form basis

The basis would be (1,0,1) and (0,1,2)

step-by-step explanation:

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to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.