WeBWork Linear Algebra - Section 3.1 Vector Spaces - Section 3.1 Vector Spaces Let u=-5-5-1]T and v=[0,5-4]T Find the vector w=2u-3v and its additive

WeBWork Linear Algebra - Section 3.1 Vector Spaces -...

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Section 3.1 Vector Spaces Let u=[-5,-5,-1]T and v=[0,5,-4]T. Find the vector w=2u-3v and its additive inverse w=[-10,-25,10]T -w=[10,25,-10]T Let x=[-5,-4]T and y=[3,-2]T. Find the vector v=5x-3y and its additive inverse v=[-34,-14]T -v=[34,14]T Let V be the set of vectors in R^2 with the following definition of addition and scalar multiplication: Addition: [x1,x2]T (+) [y1,y2]T = [0,x2+y2]T Scalar multiplication: alpha (.) [x1,x2]T = [alphax1,alphax2]T Determine which of the Vector Space Axioms are satisfied. A1. x (+) y = y (+) x for any x and y in V. A2. (x(+)y)(+)z=x(+)(y(+)z) for any x, y, and z in V A3. There in exists an element 0v in V such that x (+) 0v = x for each x in V A4. For each x in V, there exists an element -x in V such that x (+) (-x) = 0v A5. alpha (.) (x (+) y) = (alpha (.) x) (+) (alpha (.) y) for each scalar alpha and any x and y in V A6. (alpha + beta) (.) x = (alpha (.) x) (+) (beta (.) x) for any scalars alpha and beta and any x in V A7. (alphabeta) (.) x = alpha (.) (Beta (.) x) for any scalars a and B and any x in V A8. 1 (.) x = x for all x in V YES YES NO NO YES NO YES YES
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