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)

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

answer: the correct answer is -32

step-by-step explanation: