Recent questions in Matrix transformations

Linear algebraAnswered question

Oswaldo Riley 2023-03-31

I need to find a unique description of Nul A, namely by listing the vectors that measure the null space

$A=\left[\begin{array}{ccccc}1& 5& -4& -3& 1\\ 0& 1& -2& 1& 0\\ 0& 0& 0& 0& 0\end{array}\right]$

Linear algebraAnswered question

Aron Campbell 2023-03-30

T must be a linear transformation, we assume. Can u find the T standard matrix.$T:{\mathbb{R}}^{2}\to {\mathbb{R}}^{4},T\left({e}_{1}\right)=(3,1,3,1)\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}T\left({e}_{2}\right)=(-5,2,0,0),\text{}where\text{}{e}_{1}=(1,0)\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}{e}_{2}=(0,1)$

?Linear algebraAnswered question

adwelitiovb 2023-02-18

How to solve using gaussian elimination or gauss-jordan elimination, $2x-3y-2z=10$, $3x-2y+2z=0$, $4z-y+3z=-1$?

Linear algebraAnswered question

Conor Hogan 2023-01-21

What is the determinant of a $1\times 1$ matrix?

Linear algebraAnswered question

Henry Glover 2023-01-18

What is meant by the determinant of the third-order?

Linear algebraAnswered question

Jasmine Young 2023-01-06

How to find the determinant of a $2\times 3$ matrix $?$

Linear algebraAnswered question

oxidricasbt7 2022-12-20

Eigenvalues of a $2\times 2$ matrix A such that ${A}^{2}=I$

I have no idea where to begin.

I know there are a few matrices that support this claim, will they all have the same eigenvalues?

I have no idea where to begin.

I know there are a few matrices that support this claim, will they all have the same eigenvalues?

Linear algebraAnswered question

Jayden Davidson 2022-12-18

Can someone explain why a row replacement operation does not change the determinant of a matrix?

Linear algebraAnswered question

e3r2a1cakCh7 2022-12-03

The matrix equation is not solved correctly. Expain the mistake and find the correct solution. Assume that the indicated inverses exist.

$XA=B,X={A}^{-1}B$

$XA=B,X={A}^{-1}B$

Linear algebraAnswered question

atgnybo4fq 2022-11-12

Determining the Rank of a Matrix

$A=\left(\begin{array}{ccc}1& 2& 4\\ 3& 6& 5\end{array}\right)$

$A=\left(\begin{array}{ccc}1& 2& 4\\ 3& 6& 5\end{array}\right)$

Linear algebraAnswered question

Hugo Stokes 2022-10-18

Finding the inverse of linear transformation using matrix. A linear transformation represented by a matrix with respect to some random bases, how could I find the inverse of the transformation using the matrix representation?

Linear algebraAnswered question

Paloma Sanford 2022-10-13

Let $A=4\times 4$ matrix: $\left[\begin{array}{cccc}3& 2& 10& -6\\ 1& 0& 2& -4\\ 0& 1& 2& 3\\ 1& 4& 10& 8\end{array}\right]$, let $b=4\times 1$ matrix: $\left[\begin{array}{c}-1\\ 3\\ -1\\ 4\end{array}\right]$

Is $b$ in the range of linear transformation $x\to Ax$?

Is $b$ in the range of linear transformation $x\to Ax$?

Linear algebraAnswered question

Krish Schmitt 2022-09-30

Suppose $V$ is a $n$-dimensional linear vector space. $\{{s}_{1},{s}_{2},...,{s}_{n}\}$ and $\{{e}_{1},{e}_{2},...,{e}_{n}\}$ are two sets of orthonormal basis with basis transformation matrix $U$ such that ${e}_{i}=\sum _{j}{U}_{ij}{s}_{j}$.

Now consider the ${n}^{2}$ dim vector space $V\u2a02V$ (kronecker product) with equivalent basis sets $\{{s}_{1}{s}_{1},{s}_{1}{s}_{2},...,{s}_{n}{s}_{n}\}$ and $\{{e}_{1}{e}_{1},{e}_{1}{e}_{2},...,{e}_{n}{e}_{n}\}$. Now can we find the basis transformation matrix for this in terms of U?

Now consider the ${n}^{2}$ dim vector space $V\u2a02V$ (kronecker product) with equivalent basis sets $\{{s}_{1}{s}_{1},{s}_{1}{s}_{2},...,{s}_{n}{s}_{n}\}$ and $\{{e}_{1}{e}_{1},{e}_{1}{e}_{2},...,{e}_{n}{e}_{n}\}$. Now can we find the basis transformation matrix for this in terms of U?

If you are dealing with linear algebra, the chances are high that you will encounter various questions related to matrix transformation. Turning to matrix transformation examples, you will also encounter various geometric transformations, yet these will always be based on algebraic analysis and calculations. The answers that we have presented to various challenges will help you to compare our solutions with your unique matrix transformation example that deals with linear transformation and mapping. Visual assistance is also included and will be essential to see how these are built with the help of the column vectors.