Let B={(1,1,1),(4,−2,0),(0,−3,2)} and
B′={(1,0,0),(1,−2,1),(1,3,−1)} be two ordered bases for the vector
space V=R3. Find the transition...
Let B={(1,1,1),(4,−2,0),(0,−3,2)} and
B′={(1,0,0),(1,−2,1),(1,3,−1)} be two ordered bases for the vector
space V=R3. Find the transition matrix from B to B′.
Let C be the circle with radius 1 and with center (−2,1), and
let f(x,y) be...
Let C be the circle with radius 1 and with center (−2,1), and
let f(x,y) be the square of the distance from the point (x,y) to
the origin.
Evaluate the integral ∫f(x,y)ds
5. Let v1 = (1/3,−2/3,2/3), v2 = (2/3,−1/3,−2/3) and v3 =
(2/3,2/3,1/3).
(a) Verify that v1,...
5. Let v1 = (1/3,−2/3,2/3), v2 = (2/3,−1/3,−2/3) and v3 =
(2/3,2/3,1/3).
(a) Verify that v1, v2, v3 is an orthonormal basis of R 3 .
(b) Determine the coordinates of x = (9, 10, 11), v1 − 4v2 and
v3 with respect to v1, v2, v3.
Let k1dx+k2dy+k3dz be a constant 1-form and let a, b, c be any 3
point in...
Let k1dx+k2dy+k3dz be a constant 1-form and let a, b, c be any 3
point in the x,y,z space. Prove that the integral of this 1-form
from a to c is the sum of the integral from a to b plus the
integral from b to c
Using the results, prove that the amount of work done by a
constant force field in moving a particle from a to b along a path
composed of a straight line segments is...
let A (1 , 2, -3), B (2, 1, 4) and C (0, 0, 2) be...
let A (1 , 2, -3), B (2, 1, 4) and C (0, 0, 2) be three points
in R^3
a) give the parametric equation of the line orthogonal to the
plane containing A, B and C and passing through point A.
b) find the area of the triangle ABC
linear-algebra question
show clear steps and detailed solutions
solve in 30 minutes for thumbs up rating :)
Let L1 be the line passing through the point
P1(3, 5, ?5) with direction vector
d=[?1,...
Let L1 be the line passing through the point
P1(3, 5, ?5) with direction vector
d=[?1, 2, 0]T, and let
L2 be the line passing through the point
P2(?3, ?4, ?3) with the same direction
vector.
Find the shortest distance d between these two lines, and
find a point Q1 on L1 and a
point Q2 on L2 so that
d(Q1,Q2) = d. Use
the square root symbol '?' where needed to give an exact value for
your answer.
Let A be an n × n-matrix. Show that there exist B, C such that B...
Let A be an n × n-matrix. Show that there exist B, C such that B
is symmetric, C is skew-symmetric, and A = B + C. (Recall: C is
called skew-symmetric if C + C^T = 0.) Remark: Someone answered
this question but I don't know if it's right so please don't copy
his solution
Let p be an odd prime of the form p = 3k+2. Show that if a^3...
Let p be an odd prime of the form p = 3k+2. Show that if a^3 ≡
b^3 (mod p), then a ≡ b (mod p). Conclude that 1^3,2^3,…,p^3 form a
complete system of residues mod p.
Calculate ∮c(2?^2 − 3?) ?? + (?+ 2?^2)?? where C is a
closed curve (0,0) (2,0) (2,1)...
Calculate ∮c(2?^2 − 3?) ?? + (?+ 2?^2)?? where C is a
closed curve (0,0) (2,0) (2,1)
a. With direct line integral
b. With Green Theory
let
f(x,y) = 2xy+4y^2
a) find the rate of change f at the point P(3,2) in...
let
f(x,y) = 2xy+4y^2
a) find the rate of change f at the point P(3,2) in the
direction of u= [1,3]
b) in what direction does f have the maximum rate of change?
what is the maximum rate id change?