# Matrix Transformation Examples and Practice Problems

Recent questions in Matrix transformations
Faith Welch 2022-07-26

## Find the production matrix for the following input-output and demand matrices using the open model.$A=\left[\begin{array}{cc}-0.1& 0.2\\ 0.55& 0.4\end{array}\right]$$D=\left[\begin{array}{c}3\\ 4\end{array}\right]$

Jaylene Hunter 2022-07-26

## If A is an n x n matrix , where are the entries on the main diagonal of A-A^T? Justify yoyr answer.

Usman Zahid2022-07-24

## a5=0 and a15=4 what is the sum of the first 15 terms of that arithmetic sequence

Brock Byrd 2022-07-16

## Let $T:{M}_{2x2}\to {\mathbb{R}}^{3}$ have matrix $\left[T{\right]}_{B,A}=\left[\begin{array}{cccc}1& 2& 0& 1\\ 0& 1& 1& 0\\ 1& 1& -1& -1\end{array}\right]$ relative to $A=\left\{\left[\begin{array}{cc}2& 0\\ 0& 0\end{array}\right],\left[\begin{array}{cc}0& 3\\ 0& 0\end{array}\right],\left[\begin{array}{cc}0& 0\\ 5& 0\end{array}\right],\left[\begin{array}{cc}0& 0\\ 0& 6\end{array}\right]\right\}$ and $\beta =\left\{\left(1,1,1\right),\left(1,2,3\right),\left(1,4,9\right)\right\}$. Find the matrix of T relative to the bases ${A}^{\prime }=\left\{\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right],\left[\begin{array}{cc}0& 4\\ 0& 0\end{array}\right],\left[\begin{array}{cc}0& 0\\ 2& 0\end{array}\right],\left[\begin{array}{cc}0& 0\\ 0& 7\end{array}\right]\right\}$ and ${\beta }^{\prime }=\left\{\left(1,1,1\right),\left(1,0,0\right),\left(1,1,0\right)\right\}$

Joshua Foley 2022-07-16

## representative matrix of a linear transformationgiven a linear transformation: $T:{M}_{n}\left(\mathbb{C}\right)\to {M}_{n}\left(\mathbb{C}\right)$, $T\left(A\right)=A-2{A}^{T}$, what is the

Rebecca Villa 2022-07-15

## Let A be the matrix below and define a transformation $T:{\mathbb{R}}^{3}\to {\mathbb{R}}^{3}$ by $T\left(U\right)=AU.$. For each of the vectors $B$ below, find a vector $U$ such that $T$ maps $U$ to $B$, if possible. Otherwise state that there is no such $U$.$\left(\begin{array}{ccc}1& -3& 2\\ 2& -4& 4\\ 3& -8& 6\end{array}\right)=A$a) $\left(\begin{array}{c}4\\ 6\\ 11\end{array}\right)=B$b) $\left(\begin{array}{c}-3\\ -2\\ -7\end{array}\right)=B$

uplakanimkk 2022-07-14

## Suppose $T$ is a transformation from ${\mathbb{R}}^{2}$ to ${\mathbb{R}}^{2}$. Find the matrix $A$ that induces $T$ if $T$ is the (counter-clockwise) rotation by $\frac{3}{4}\pi$.how to begin to find a matrix that is 2x2 for this question.

Willow Pratt 2022-07-12

## Let $A$ be the set of all $n×n$ symmetric real matirix and $f\in C\left(\mathbb{R},A\right)$. Then whether there is a $g\in C\left(\mathbb{R},O\left(n\right)\right)$ such that for all $t\in \mathbb{R}$, $g\left(t{\right)}^{-1}f\left(t\right)g\left(t\right)$ is a diagonal matrix?

Jamison Rios 2022-07-12

## Can't figure out this transformation matrix1) The positive z axis normalized as Vector(0,0,1) has to map to an arbitrary direction vector in the new coordinate system Vector(a,b,c)2) The origin in the original coordinate system has to map to an arbitrary position P in the new coordinate system.3) This might be redundant but the positive Y axis has to map to a specific direction vector(d,e,f) which is perpendicular to Vector(a,b,c) from before.So my question is twofold: 1) How would I go about constructing this transformation matrix and 2) Is this enough data to ensure that any arbitrary vector in coordinate system 1 will be accurately transformed in coordinate system 2?

ntaraxq 2022-07-12

## How can one prove the following identity of the cross product? $\left(Ma\right)×\left(Mb\right)=det\left(M\right)\left({M}^{\mathrm{T}}{\right)}^{-1}\left(a×b\right)$ $a$ and $b$ are 3-vectors, and $M$ is an invertible real $3×3$ matrix.

mistergoneo7 2022-07-10

## I'd like to be able to enter a vector or matrix, see it in 2-space or 3-space, enter a transformation vector or matrix, and see the result. For example, enter a 3x3 matrix, see the parallelepiped it represents, enter a rotation matrix, see the rotated parallelepiped.

Kristen Stokes 2022-07-10

## Let $M$ be a transformation matrix $B\to {B}^{\prime }$discovered that ${M}^{-1}$ is the opposite transformation.What makes it true?

ntaraxq 2022-07-10

## Consider the transformation $T:{\mathbb{R}}^{3}\to {\mathbb{R}}^{2}$ defined by:$T\left(x\right)=T\left(\begin{array}{c}{x}_{1}\\ {x}_{2}\\ {x}_{3}\end{array}\right)=\left(2{x}_{1}+{x}_{3}\right)\left(\begin{array}{c}1\\ 2\end{array}\right)+\left({x}_{2}-3{x}_{3}\right)\left(\begin{array}{c}-1\\ 1\end{array}\right)$1a) determine the matrix of the above transformation1b) determine the reduced row echelon form of the matrix found in 1a 1c) based on your answer to part 1b, is the transformation T onto?1d) based on your answer to part 1b, is the transformation T one-to-one?1e) based on your answer to part 1b, determine the set of vectors $x$ in ${\mathbb{R}}^{3}$ for which $T\left(x\right)=0$. Write your answer in parametric vector form

prirodnogbk 2022-07-09

## Can't figure out this transformation matrix1) The positive z axis normalized as Vector(0,0,1) has to map to an arbitrary direction vector in the new coordinate system Vector(a,b,c)2) The origin in the original coordinate system has to map to an arbitrary position P in the new coordinate system.3) This might be redundant but the positive Y axis has to map to a specific direction vector(d,e,f) which is perpendicular to Vector(a,b,c) from before.So my question is twofold: 1) How would I go about constructing this transformation matrix and 2) Is this enough data to ensure that any arbitrary vector in coordinate system 1 will be accurately transformed in coordinate system 2?

uplakanimkk 2022-07-09

## Find the transformation matrixLet $B=\left\{2x,3x+{x}^{2},-1\right\},{B}^{\prime }=\left\{1,1+x,1+x+{x}^{2}\right\}$Need to find the transformation matrix from $B$ to ${B}^{\prime }$.I know that:$\left(a{x}^{2}+bx+c{\right)}_{B}=\left(\frac{b-3c}{2},c,-a\right)$$\left(a{x}^{2}+bx+c{\right)}_{{B}^{\prime }}=\left(a-b,b-c,c\right)$How to proceed using this info in order to find the transformation matrix?

kramberol 2022-07-08