27. Let S be the set of all vectors both of y in R' such that x + y -z = 0 and 2x – 3y + 2z = 0. Show that S with the standard componentwise operations is a vector space. %3D -

express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is linearly independent. If yes, show work, if no state a linear combination among the vectors of the list that adds up to a vector in the list. I am having trouble grasping the concept so if anyone can explain this problem I'd appreciate it.

. Assuming the +x-axis is horizontal to the right for the vectors in the following figure, find the following scalar products:  (a)   →A · →C  ; (b) →A · →F;  (c)   →D  ·  →C  ;  (d) →A · (→F   + 2 →C); (e) ^i · →B; (f) ^j · →B;  (e) (3 ^i − ^j) · →B, and (h) B^ · B→.

Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  For each vector b, which is an element of R^2, there is one and only one vector x, which in an element of R^2, such that A*vector x=vector b.

(a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+ 3b.

I have a set of vectors in R^2(i.e. two-dimensional vectors) such that the scalarproduct (the same as the inner product, or dot product) of any two of the vectors is negative.What is the maximum number of vectors that can be in my set?

Let V₁, V2, V3 be the vectors in R³ defined by 18 ---D V₁ = -6 V2 = -14 V3 = 20 (a) is (V1, V2, Vs} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V₂, and V3 0 (c) Type the dimension of span {V1, V2, V3}: Note: You can earn partial credit on this problem. -25 -18] 0=v₁+√₂+vs (b) Is (v1, vs} linearly Independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁ and V3. 0=v₁+v₁ V3

If a = (4, 0, -1), find a vector b such that comp_b = 3. b =

Let v1 vector=[−4  h] and v2 vector =[−10   20]   (check image for reference) Then span(v1 vector,v2 vector)=R^2 as long as h≠  (If there are no values of hh that make the set fail to span R^2, enter "NONE". If the set fails to span R^2 for all values of hh enter "ALL".)