$\left(\begin{array}{ccc}1& 3& 3\\ 2& 6& -3.5+k\end{array}\right)$

is onto if and only if $k\ne $

Boilanubjaini8f
2022-06-26
Answered

A linear transformation $T:{\mathbb{R}}^{3}\to {\mathbb{R}}^{2}$ whose matrix is

$\left(\begin{array}{ccc}1& 3& 3\\ 2& 6& -3.5+k\end{array}\right)$

is onto if and only if $k\ne $

$\left(\begin{array}{ccc}1& 3& 3\\ 2& 6& -3.5+k\end{array}\right)$

is onto if and only if $k\ne $

You can still ask an expert for help

grcalia1

Answered 2022-06-27
Author has **23** answers

$T$ takes in a column vector $({a}_{1},{a}_{2},{a}_{3}{)}^{T}$, i.e. an element of ${\mathbf{R}}^{3}$, and sends it to

$\left(\begin{array}{ccc}1& 3& 3\\ 2& 6& -3.5+k\end{array}\right)\left(\begin{array}{c}{a}_{1}\\ {a}_{2}\\ {a}_{3}\end{array}\right).$

Convince yourself that this results in a $2\times 1$ matrix, i.e. an element of ${\mathbf{R}}^{2}$

$\left(\begin{array}{ccc}1& 3& 3\\ 2& 6& -3.5+k\end{array}\right)\left(\begin{array}{c}{a}_{1}\\ {a}_{2}\\ {a}_{3}\end{array}\right).$

Convince yourself that this results in a $2\times 1$ matrix, i.e. an element of ${\mathbf{R}}^{2}$

asked 2021-09-13

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

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 2021-09-18

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

asked 2021-01-24

It can be shown that the algebraic multiplicity of an eigenvalue lambda is always greater than or equal to the dimension of the eigenspace corresponding to lambda. Find h in the matrix A below such that the eigenspace for lambda = 5 is two-dimensional:
$A=\left[\begin{array}{cccc}5& -2& 6& -1\\ 0& 3& h& 0\\ 0& 0& 5& 4\\ 0& 0& 0& 1\end{array}\right]$

asked 2022-01-29

Matrix transformation

$f:{\mathbb{R}}^{3}\to {\mathbb{R}}^{3}$

$\left(\begin{array}{ccc}4& 1& 3\\ 2& -1& 3\\ 2& 2& 0\end{array}\right)$

Establish x,y and z such that,

$f\left(\begin{array}{c}x\\ y\\ z\end{array}\right)$

Do I just need to multiply the values of f for the$3\times 3$ matrix? What does this mean overall?

Establish x,y and z such that,

Do I just need to multiply the values of f for the

asked 2022-06-28

Transformation matrix for matrix indices to cartesian coordinates

(1,1) (1,2) (1,3)(2,1) (2,2) (2,3)(3,1) (3,2) (3,3)

This is an example 3x3 matrix. In corresponding cartesian coordinate system, the representation would be:

(-1,1) (0,1) (1,1)(-1,0) (0,0) (1,0)(-1,1) (0,-1) (1,-1)

Say, I have any square matrix with dimension-N, where N is odd. I need a generic transformation matrix such that I can get a vector as cartesian coordinates from matrix indices. Does such a function already exist? How should I go ahead in implementing this?

(1,1) (1,2) (1,3)(2,1) (2,2) (2,3)(3,1) (3,2) (3,3)

This is an example 3x3 matrix. In corresponding cartesian coordinate system, the representation would be:

(-1,1) (0,1) (1,1)(-1,0) (0,0) (1,0)(-1,1) (0,-1) (1,-1)

Say, I have any square matrix with dimension-N, where N is odd. I need a generic transformation matrix such that I can get a vector as cartesian coordinates from matrix indices. Does such a function already exist? How should I go ahead in implementing this?

asked 2021-12-05

Use an inverse matrix to solve each system of linear equations.

2x-y=-1

2x+y=-3

2x-y=-1

2x+y=-3