Let θ : R^4 → R defined by θ(u) = sup{u1|, |u4|}. Determine if θ is a norm, a seminorm or none of the two for R^4

Q: Let L be the line in R2 through the points [:] } Find a linear functional f and a real number d such…

A: First, we will find the equation of a line given two points.

Q: Let x = [2] Show that the transformation T defined by T(x) = Edit Insert Formats BI Ụ X, xỉ A 블로 N H…

A: We will show that the given transformation is not Linear.

Q: If u and v are two vectors in opposite directions, then : Select one: a. u equals a negative…

A:

Q: Prove that ATM <m EQtm: (a) Construct a mapping reduction from ATM to EQtm. (b) Prove that the…

A:

Q: 1. Let f: R" → R be the function f(x) = cx+b for some fixed vector c ER" and scalar b. Show that f…

A:

Q: Let f(x, y, z) = x²y³ + zª and x = s², y = st², and z = (a) Calculate the primary derivatives - af…

A: fx, y, z=x2y3+z4  &amp;  x=s2, y=st2,  &amp;  z=s2t a). ∂f∂x=∂∂xx2y3+z4=y3·2x+0=2xy3…

Q: Show that the parametric curve r(t)= , t [-1,1] is smooth and compute its lengh

A: The given parametric curve is: r(t)=t1+t2, 11+t2 ;          t∈-1, 1

Q: Show that the gradient vector is perpendicular to the tangent at a point of an isovalue curve

A: According to question                                     Let,  w=f(x, y, z)  be a function in…

Q: Let T be a linear transformation that maps R" onto R". Show that T-1 exists and maps R" onto R". Is…

A: Given T be a linear transformation that maps Rn  onto Rn. We have to show that T-1 exist and maps Rn…

Q: Let fi(x) E Fun (R,R) be the constant function I, wheret ficx)=1 for all xG RRe Prove that S { sec?…

A: Given: fx∈funℝ, ℝ is a constant function. such that: fx=1……1 S=sec2x, tan2x, fx

Q: Given the vector-valued function r (t) = e-t i +t j +(tan t) k Find: a) r'(t) b) r"(t) c) r'(t) .…

A:

Q: II. Decide which of the following are subspaces of corresponding vector spaces: C R?

A: Vector space.

Q: 10. Show that 1/x, x are linearly independent on (0, 0).

A:

Q: Create a vector-valued function whose graph is an ellipse, centered at (1, 2) with horizontal major…

A: