Ashlynn Hale
2022-08-10
Answered

An augmented matrix of a system of equations has been transformed by row operations into the 3 equations in 3 variables matrix below. State the solution to this system as (x,y,z) Enter your answer as an ordered triple within parenthesis separated by commas (x,y,z). Avoid entering spaces and decimal points Use fractions if relevant.

$$\left[\begin{array}{ccccc}1& 0& 0& \vdots & -3\\ 0& 1& 0& \vdots & \frac{2}{3}\\ 0& 0& 1& \vdots & \frac{1}{4}\end{array}\right]$$

You can still ask an expert for help

Marlie Frazier

Answered 2022-08-11
Author has **14** answers

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

$=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}-3\\ 2/3\\ 1/4\end{array}\right]$

x=-3, y=2/3, z=1/4

$=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}-3\\ 2/3\\ 1/4\end{array}\right]$

x=-3, y=2/3, z=1/4

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 2022-06-06

What is the transformation matrix?

In ${\mathbb{R}}^{\mathbb{2}}$ a basis is given $a=({a}_{1},{a}_{2})$ where:

${a}_{1}=(1,-1)$

${a}_{2}=(0,1)$

For $f:{\mathbb{R}}^{\mathbb{2}}\to {\mathbb{R}}^{\mathbb{2}}$ it is known:

$f({a}_{1})=-6\cdot {a}_{1}$

$f({a}_{2})=1\cdot {a}_{2}$

Determine the matrix of transformation with regards to the standard e-basis.

In ${\mathbb{R}}^{\mathbb{2}}$ a basis is given $a=({a}_{1},{a}_{2})$ where:

${a}_{1}=(1,-1)$

${a}_{2}=(0,1)$

For $f:{\mathbb{R}}^{\mathbb{2}}\to {\mathbb{R}}^{\mathbb{2}}$ it is known:

$f({a}_{1})=-6\cdot {a}_{1}$

$f({a}_{2})=1\cdot {a}_{2}$

Determine the matrix of transformation with regards to the standard e-basis.

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 2022-08-31

Find the inverse, if it exists, for the given matrix

$\left[\begin{array}{cc}3& 2\\ 2& 5\end{array}\right]$

$\left[\begin{array}{cc}3& 2\\ 2& 5\end{array}\right]$

asked 2022-07-12

How can one prove the following identity of the cross product?

$(Ma)\times (Mb)=det(M)({M}^{\mathrm{T}}{)}^{-1}(a\times b)$

$a$ and $b$ are 3-vectors, and $M$ is an invertible real $3\times 3$ matrix.

$(Ma)\times (Mb)=det(M)({M}^{\mathrm{T}}{)}^{-1}(a\times b)$

$a$ and $b$ are 3-vectors, and $M$ is an invertible real $3\times 3$ matrix.