Kyran Hudson
2021-01-05
Answered

Find a set of vectors that spans the plane $P1:2x+3y-z=0$

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SoosteethicU

Answered 2021-01-06
Author has **102** answers

Note that if

It follows that the vectors (1,0,2), (0,1,3) spans the plane P1.

asked 2021-09-22

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at

asked 2021-06-01

Find the vectors T, N, and B at the given point.

$r(t)=<{t}^{2},\frac{2}{3}{t}^{3},t>$ and point $<4,-\frac{16}{3},-2>$

asked 2021-05-14

Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR

Consider the points below

P(1,0,1) , Q(-2,1,4) , R(7,2,7)

a) Find a nonzero vector orthogonal to the plane through the points P,Q and R

b) Find the area of the triangle PQR

Consider the points below

P(1,0,1) , Q(-2,1,4) , R(7,2,7)

a) Find a nonzero vector orthogonal to the plane through the points P,Q and R

b) Find the area of the triangle PQR

asked 2021-09-21

Consider the linear system

a) Find the eigenvalues and eigenvectors for the coefficient matrix

b) For each eigenpair in the previos part, form a solution of

c) Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solution? No, it is not a fundamental set.

asked 2022-05-17

I have to find components of a matrix for 3D transformation. I have a first system in which transformations are made by multiplying:

${M}_{1}=[Translation]\times [Rotation]\times [Scale]$

I want to have the same transformations in an engine who compute like this:

${M}_{2}=[Rotation]\times [Translation]\times [Scale]$

So when I enter the same values there's a problem due to the inversion of translation and rotation.

How can I compute the values in the last matrix ${M}_{2}$ for having the same transformation?

${M}_{1}=[Translation]\times [Rotation]\times [Scale]$

I want to have the same transformations in an engine who compute like this:

${M}_{2}=[Rotation]\times [Translation]\times [Scale]$

So when I enter the same values there's a problem due to the inversion of translation and rotation.

How can I compute the values in the last matrix ${M}_{2}$ for having the same transformation?

asked 2022-03-30

If u, v, w ∈ R n , then span(u, v + w) = span(u + v, w)

asked 2022-01-31

How do we know that S must be induced by some matrix B?

Functions$T:{\mathbb{R}}^{n}\to {\mathbb{R}}^{m}$ are called transformations from $\mathbb{R}}^{n$ to $\mathbb{R}}^{m$

A transformation$T:{\mathbb{R}}^{n}\to {\mathbb{R}}^{n}$ has an inverse if there is some transformation S such that $T\circ S=S\circ T={1}_{{\mathbb{R}}^{n}}$

Let$T={T}_{A}:{\mathbb{R}}^{n}\to {\mathbb{R}}^{n}$ denote the matrix transformation induced by the $n\times n$ matrix A, that is $T\left(x\right)=Ax$

We have:

$BA\mathbf{x}=S\left[T\left(\mathbf{x}\right)\right]=(S\circ T)\mathbf{x}={1}_{{\mathbb{R}}^{\mathbb{n}}}\left(\mathbf{x}\right)=\mathbf{x}={I}_{n}\mathbf{x}$

Functions

A transformation

Let

We have: