The matrix:

Miguel Davenport
2022-01-30
Answered

Find invariant points under matrix transformation

The matrix:

$Q=\left[\begin{array}{cc}-1& 2\\ 0& 1\end{array}\right]$

The matrix:

You can still ask an expert for help

asked 2021-09-18

Find an explicit description of Nul A by listing vectors that span the null space.

asked 2021-06-13

For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A.

$A=\left[\begin{array}{cccc}2& 3& 5& -9\\ -8& -9& -11& 21\\ 4& -3& -17& 27\end{array}\right]$

Find a nonzero vector in Nul A.

$A=\left[\begin{array}{c}-3\\ 2\\ 0\\ 1\end{array}\right]$

Find a nonzero vector in Nul A.

asked 2021-09-13

Assume that A is row equivalent to B. Find bases for Nul A and Col A.

asked 2022-01-20

Find matrix of linear transformation

A linear transformation

$T:{\mathbb{R}}^{2}\to {\mathbb{R}}^{2}$

is given by

$T\left(i\right)=i+j$

$T\left(j\right)=2i-j$

A linear transformation

is given by

asked 2022-06-16

Here's the question:

Let $A=\left[\begin{array}{cc}5& -3\\ 2& -2\end{array}\right]$, which is a linear transformation ${\mathbb{R}}^{2}\to {\mathbb{R}}^{2}$. Find the matrix representing the transformation with respect to basis $\left[\begin{array}{cc}3& 1\\ 1& 2\end{array}\right]$.

I understand how to solve the question. You would do ${B}^{-1}AB$. I did the multiplication and got $\left[\begin{array}{cc}20& 0\\ 0& -5\end{array}\right]$. The author of the document got the same answer but then multiplied the matrix by 1/5 to get $\left[\begin{array}{cc}4& 0\\ 0& -1\end{array}\right]$. Why is he allowed to do that?

Let $A=\left[\begin{array}{cc}5& -3\\ 2& -2\end{array}\right]$, which is a linear transformation ${\mathbb{R}}^{2}\to {\mathbb{R}}^{2}$. Find the matrix representing the transformation with respect to basis $\left[\begin{array}{cc}3& 1\\ 1& 2\end{array}\right]$.

I understand how to solve the question. You would do ${B}^{-1}AB$. I did the multiplication and got $\left[\begin{array}{cc}20& 0\\ 0& -5\end{array}\right]$. The author of the document got the same answer but then multiplied the matrix by 1/5 to get $\left[\begin{array}{cc}4& 0\\ 0& -1\end{array}\right]$. Why is he allowed to do that?

asked 2022-06-22

Consider the transformation $T:{P}_{2}\to {P}_{2}$, where ${P}_{2}$ is the space of second-degree polynomials matrices, given by $T(f)=f(-1)+f\prime (-1)(t+1)$. Find the matrix for this transformation relative to the standard basis $\mathfrak{A}=\{1,t,{t}^{2}\}$. Can someone explain to me how to find the matrix of the transformation

asked 2022-05-20

How do I use matrix multiplication to find the reflection of (-1,2) about the x axis, y axis and the line y=x?