Which one of the following is a linear transformation? O F(x, y) = xy O F(x,y)...
What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2)? -8 -3 4 12 b) c) d) e) none of these 113 113 V13 113 a) o What is the average rate of change of z = f(x, y) = x² + xy(with respect to horizontal distance) as one travels from (2,1) to (4,-2)? 2 5 12 c) d) e) none of...
linear algebra Determine whether the function is a linear transformation. T: R2 R3, T(x, y) = (x,xy, vy) O linear transformation O not a linear transformation
which of the following is a potential function for F(x,y,z)= < y2 +y?ex?,x2 + 2ye*?,xy + xy?e *V> f(x,y,z) = xyz + y2exyz f(x,y,z) = xyz + y2e*+2 b. F(x,y,z) has a potential function but it is not one of the other choices. F(x,y,z) does not have a potential function. d. f(x,y,z) = xyz + y2exZ e.
Let f(x, y, z) = yln(zx) + ztan(xy). Find the linear approximation to f at the point (1,0,1). Use this linear approximation to approximate s(5,55 *). Show all of your work to obtain the linear approximation.
Given the linear transformation T:RPR:T[(x, y, z)] = (4x+Z, -34 +2 ) and basis B4={(2,4,-1); (0,1,-2); (0,2,-2)} and B2 = {(-3,0);(-2,11} Find element Q13 of the transformation matrix
Determine whether or not the following transformation T :V + W is a linear transformation. If T is not a linear transformation, provide a counter example. If it is, then: (i) find the nullspace N(T) and nullity of T, (ii) find the range R(T) and rank of T, (iii) determine if T is one-to-one, (iv) determine if T is onto. : (a) T: R3 + R2 defined by T(x, y, z) = (2x, y, z) (b) T: R2 + R2...
Problem 2 [10pts] Let f : R3 + R2 be a linear transformation given by f((x, y, z) = (–2x + 2y +z, -x +2y). Find the matrix that corresponds to f with respect to the canonical bases of R3 and R2.
If z = xy + xf (?), then xgie + y + z = xy. O True O Falsem 11== f ($x + 2), then 29. – 3.3 -1. then O True False If z = , then x2 + y a = 2 True 0 False If w = f (xz, yz), then xy + y O True 0 False
3. Consider two random variables X and Y with the joint probability density (a)o elsewhere which is the sane asin Question I. Now let Z = XY 2 and U = X be a joint transformation of (X, Y). (a) Find the support of (Z, U) (b) Find the inverse transformation (c) Find the Jacobian of the inverse transformation. (d) Find the joint pdf of (Z, U) (e) Find the pdf of Z XY from the joint pdf of (Z,...
9. What is the instantaneous rate of change of 2 = f(x,y) = x + xy (with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2) ? e) none of these V13 12 -8 V13 13