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**limpfisch**- Replies: 1

let a,b be members of a group (G,*). Show that if (a*b) inverse = (a inverse)*(b inverse) then a*b = b*a

**limpfisch**- Replies: 1

Perform a householder transformation followed by a plane rotation to trasform the following matrix A into an upper triangular matrix R.

A= 4 3 0

4 3 6

2 6 5

This is not covered in my textbook

**limpfisch**- Replies: 0

Let S = {(1234),(4321)}

and W the subspace of R4 generated by S.

Find an orthogonal basis of the orthogonal complement W^ of W

Find the shortest distance from u+(12-21) to W^

Obviously the vectors of S are meant to be written as one colum instead of 4.

Thanks.

**limpfisch**- Replies: 0

Show that if A and B represent reflections in R2 or R3, then AB represents a rotation.

I can invision this but i'm not sure how to show it.

**limpfisch**- Replies: 2

Let B = {u1,u2} be a basis of a vector space V

Show that C = {v1 = 2u1 - 3u2, v2 = 2u1 + 2u2} is also a basis of V.

Also, what is the change of basis matrix from B to C?

Thanks very much for any help you give me.

**limpfisch**- Replies: 1

Let B= {(2 -1),(3 -1)

Let C= {(1 2),(2 3)

Find the change of basis matrix from C to B.

I've been sick the last week so haven't attended lectures and have an assignment due. The notes for this course are terrible and do not help me with this so please explain how to do this thanks.

**limpfisch**- Replies: 1

Let R1 denote the rectangle [0, 5] × [4, 4], R2 the rectangle [0, 5] × [0, 4], and R3 the

rectangle [5, 0] × [4, 0]. Suppose that ∫∫R2 f (x, y)dA = 10 , that ∫∫R3 f (x, y)dA = 24

and that f (−x, y) = − f (x, y) for all (x, y). Evaluate ∫∫R1 f (x, y)dA

really not sure on the approach here.

**limpfisch**- Replies: 1

r(t) = ((4cost)^3, (4sint)^3) for -pi<=pi

i tried just finding T(t) by using r'(t)/|r'(t)| but i keep getting a giant mess which is no good given i have to find the normal vector and curvature later. Please help.

**limpfisch**- Replies: 1

On a certain mountain, the elevation z above a point (x, y) in a horizontal xy-plane

at sea level is z = 2500 - x^2/10 - y^2/5 metres. The positive x-axis points east; the

positive y-axis points north. Suppose that a climber is at the point (15, 10, 2457.5)

if the climber moves southease, what rate will the climber begin to descend at?

i calculated the gradients in the zx direction and in the zy direction, but i'm not sure what the continuation is.

**limpfisch**- Replies: 8

Which spring requires more material to make it, one of radius 5 cm and height 4 cm

that makes three complete turns or one of radius 3 cm and height 4 cm that makes

five complete turns?

i thought i did it right but logically my answer can't be.

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