are the columns

of the

Tobias Ali
2021-02-19
Answered

To explain^ Why the beta-coordinate vectors of $\beta ={b}_{1},...,{b}_{n}$

are the columns${e}_{1},...,{e}_{n}$

of the$n\times n$ identity matrix.

are the columns

of the

You can still ask an expert for help

Benedict

Answered 2021-02-20
Author has **108** answers

Consider a vector x in V such that,

The coordinates of x relative to basis

also called beta-coordinates of x are given by,

Since

Thus, the vectors

Therefore, if any vector

That is, an arbitrary vector

can be written as

Here, k varies from 1 to n.

Thus, the beta-coordinates of

in this case are

The matrix formed by these beta-coordinates is

That is, beta-coordinate vectors of

are the columns

asked 2020-11-02

Find inequalities that describe the solid and state the coordinate system used. Position the solid on the coordinate system such that the inequalities are as simple as possible. "The solid that remains after a hole 1 inch in diameter is drilled through the center of a sphere 6 inches in diameter "

asked 2021-03-05

Consider the solid that is bounded below by the cone $z=\sqrt{3{x}^{2}+3{y}^{2}}$

and above by the sphere${x}^{2}+{y}^{2}+{z}^{2}=16.$ .Set up only the appropriate triple integrals in cylindrical and spherical coordinates needed to find the volume of the solid.

and above by the sphere

asked 2021-09-19

Find Maximum Volume of a rectangular box that is inscribed in a sphere of radius r.

The part i do not get the solutions manual got$2x,\text{}2y$ , and $2z$ as the volume. Can you explain how the volume of the cube for this problem is $v=8xyz?$

The part i do not get the solutions manual got

asked 2020-10-26

Plotting points and finding distance in three dimensions. Two points P and $\underset{\u2015}{O}$ are given.

(a) Plot P and$\underset{\u2015}{O}$ .

(b) Find the distance between P and$\underset{\u2015}{O}.$

$P(3,1,0),\underset{\u2015}{O}(-1,2,-5)$

(a) Plot P and

(b) Find the distance between P and

asked 2021-01-28

Plot the given point $(-4,0)$ in a rectangular coordinate system.

asked 2020-12-29

Describe in words the region of ${R}^{3}$ represented by the equation(s) or inequality.

${x}^{2}+{y}^{2}=4$

asked 2021-02-15

A subset ${u}_{1},...,{u}_{p}$ in V is linearly independent if and only if the set of coordinate vectors

$[{u}_{1}{]}_{\beta},...,[{u}_{p}{]}_{\beta}$

is linearly independent in${R}^{n}$

is linearly independent in