Braxton Pugh
2020-11-08
Answered

Whether the statement "I need to be able to graph systems of linear inequalities in order to solve linear programming problems" makes sense or not.

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firmablogF

Answered 2020-11-09
Author has **92** answers

Let $z=ax\text{}+by$ be an objective function that depends on x and y. Also, z is subject to a number of constraints on x and y. If a maximum or minimum value of z exist, the linear programming problem can be solved as follows:

Step1: Graph the system of inequalities that represents the constraints.

Step 2: Obtain the value of the objective function at each corner of the graphed region.

The maximum and ninimum of the objective function will occur at one or more corner points.

Thus, to find the maximum or minimum values of a linear programming problem, the coordinates of each vertex from the graph representing the constraints need to be substituted in the objective function.

Hence, the given statement makes sense.

Step1: Graph the system of inequalities that represents the constraints.

Step 2: Obtain the value of the objective function at each corner of the graphed region.

The maximum and ninimum of the objective function will occur at one or more corner points.

Thus, to find the maximum or minimum values of a linear programming problem, the coordinates of each vertex from the graph representing the constraints need to be substituted in the objective function.

Hence, the given statement makes sense.

asked 2022-06-23

Need to find a matrix transformation that takes a (non-square) matrix and within each of its rows keeps the first nonzero element in that row and zeros out the rest of the entries within that row.

I tried to solve the linear matrix equation AX = B to get the matrix transformation A as A = B X^T (XX^T)^{-1} , where X is the matrix to be transformed as such, and B is the desired output matrix (X with only its first nonzero element in each row) but I look for a more straightforward and possibly more elegant way to do it. I appreciate creative answers!

I tried to solve the linear matrix equation AX = B to get the matrix transformation A as A = B X^T (XX^T)^{-1} , where X is the matrix to be transformed as such, and B is the desired output matrix (X with only its first nonzero element in each row) but I look for a more straightforward and possibly more elegant way to do it. I appreciate creative answers!

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What is the Use for transformations of a matrix?

asked 2022-06-24

Linear transformation and its matrix

two bases:

$A=\{{v}_{1},{v}_{2},{v}_{3}\}$ and $B=\{2{v}_{1},{v}_{2}+{v}_{3},-{v}_{1}+2{v}_{2}-{v}_{3}\}$

There is also a linear transformation: $T:{\mathbb{R}}^{3}\to {\mathbb{R}}^{3}$

Matrix in base $A$:

${M}_{T}^{A}=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 1& 1& 0\end{array}\right]$

Now I am to find matrix of the linear transformation $T$ in base $B$.

I have found two transition matrixes (from base $A$ to $B$ and from $B$ to $A$):

${P}_{A}^{B}=\left[\begin{array}{ccc}2& 0& -1\\ 0& 1& 2\\ 0& 1& -1\end{array}\right]$

$({P}_{A}^{B}{)}^{-1}={P}_{B}^{A}=\left[\begin{array}{ccc}\frac{1}{2}& \frac{1}{6}& \frac{-1}{6}\\ 0& \frac{1}{3}& \frac{2}{3}\\ 0& \frac{1}{3}& \frac{-1}{3}\end{array}\right]$

How can I find ${M}_{T}^{B}$?

two bases:

$A=\{{v}_{1},{v}_{2},{v}_{3}\}$ and $B=\{2{v}_{1},{v}_{2}+{v}_{3},-{v}_{1}+2{v}_{2}-{v}_{3}\}$

There is also a linear transformation: $T:{\mathbb{R}}^{3}\to {\mathbb{R}}^{3}$

Matrix in base $A$:

${M}_{T}^{A}=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 1& 1& 0\end{array}\right]$

Now I am to find matrix of the linear transformation $T$ in base $B$.

I have found two transition matrixes (from base $A$ to $B$ and from $B$ to $A$):

${P}_{A}^{B}=\left[\begin{array}{ccc}2& 0& -1\\ 0& 1& 2\\ 0& 1& -1\end{array}\right]$

$({P}_{A}^{B}{)}^{-1}={P}_{B}^{A}=\left[\begin{array}{ccc}\frac{1}{2}& \frac{1}{6}& \frac{-1}{6}\\ 0& \frac{1}{3}& \frac{2}{3}\\ 0& \frac{1}{3}& \frac{-1}{3}\end{array}\right]$

How can I find ${M}_{T}^{B}$?

asked 2022-03-27

I need solution of Q2 of given assignment

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Find the linearization L(x) of the function at a. $f\left(x\right)={x}^{4}\mp 3{x}^{2}$ , $a=-1$

asked 2021-09-22

Let S be the parallelogram determined by the vectors

and

and let

Compute the area of the image of S under the mapping

asked 2022-06-20

Inverse of transformation matrix

For the following 3D transfromation matrix M, find its inverse. Note that M is a composite matrix built from fundamental geometric affine transformations only. Show the initial transformation sequence of M, invert it, and write down the final inverted matrix of M.

$M=\left(\begin{array}{cccc}0& 0& 1& 5\\ 0& 3& 0& 3\\ -1& 0& 0& 2\\ 0& 0& 0& 1\end{array}\right)$

For the following 3D transfromation matrix M, find its inverse. Note that M is a composite matrix built from fundamental geometric affine transformations only. Show the initial transformation sequence of M, invert it, and write down the final inverted matrix of M.

$M=\left(\begin{array}{cccc}0& 0& 1& 5\\ 0& 3& 0& 3\\ -1& 0& 0& 2\\ 0& 0& 0& 1\end{array}\right)$