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:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

answer: r there any options?

step-by-step explanation: