V = M2x2 (R) let M = { A€ V A = A²} N = { A = V A = -A ² } Subset of the vector space V V = MON prove that
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- Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}Show that the vectors are linearly dependent or linearly independent. note: {2t^2 − 1, t + 1},P2:The space of all polynomials with a degree less than 2 and 2What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 = (14, 2, 8)
- Let ^-40 A Find a unit vector x whose first component is positive at which Ax has maximum length. Enter the components of x (in order) into the answer box below, separated with a comma.Let u1 = 3 Uz = then write x as sum of two vectors Uz = X = -3 1 on in span {u1} and other one in span {u2, U3,} (a) 1 X = -2 (b) X = 3 -3 3 2 (©Q* -2 + -3 (c) (d) X = 2. 1101 +For which real values of A do the following vectors form a linearly dependent set in R³? V₁ = 1₂ V2= V3 X₁ = 1 3' 3 1 (-₁^,-) = 1 3 2 3 - 1/3,^) A₂ =
- use the vectors u=<5,5> and v=<-5,4> to find the indicated quantity 3u * v= State whether the result is a vector or a scalar.Find a unit vector (i.) parallel to the graph of f at the given point f(x)=x^2+2x-4, (2,4) (ii.) perpendicular to the graph of f at the given point. f(x)=x^2+2x-4, (2,4)Determine the domain of the vector function r(t)=(t^2−4)/(t−2)i+sqrt(t+5)j+(e^t)* k Select one: a. [−5,2)∪(2,∞) b. [−5,∞) c. (−∞,∞) d. (−5,2)∪(2,∞) e. (−∞,2)∪(2,∞)
- b / Let u and v be a nonzero vectors in 3- space, and let 6 be the angle between these vectors when they are positioned so their initial points coincide. Prove that ux v= sin @Find the scalar product of x and y x =(-1, 0, 2) and y =(-7, 7, 3)Determine: if W = the set of all vectors in R^2 whose second component is the square of the first. Is a subspace
