- #1

WK95

- 139

- 1

Mod note: fixed an exponent (% --> 5) on the transformation definition.

A is a (4x5)-matrix over R, and L_A:R^5 --> R^4 is a linear transformation defined by L_a(x)=Ax. Find the basis for the range of L_A.

##A = \begin{bmatrix}1 & 2 & 3 & 4 & 5 \\2 & 3 & 4 & 5 & 6 \\3 & 4 & 5 & 6 & 7 \\4 & 5 & 6 & 7 & 8 \end{bmatrix}##

##A = \begin{bmatrix}1 & 2 & 3 & 4 & 5 & b_{1} \\2 & 3 & 4 & 5 & 6 & b_{2} \\3 & 4 & 5 & 6 & 7 & b_{3} \\4 & 5 & 6 & 7 & 8 & b_{4} \end{bmatrix} ##

##A = \begin{bmatrix}1 & 0 & -1 & -2 & -3 & -3b_{1}+2b_{2} \\0 & -1 & -2 & -3 & -4 & -2b_{1}+b_{2} \\0 & 0 & 0 & 0 & 0 & b_{1}-2b_{2}+b_{3} \\0 & 0 & 0 & 0 & 0 & 2b_{1}-3b_{2}+b_{4} \end{bmatrix}##

Where do I go from there?

## Homework Statement

A is a (4x5)-matrix over R, and L_A:R^5 --> R^4 is a linear transformation defined by L_a(x)=Ax. Find the basis for the range of L_A.

## Homework Equations

## The Attempt at a Solution

##A = \begin{bmatrix}1 & 2 & 3 & 4 & 5 \\2 & 3 & 4 & 5 & 6 \\3 & 4 & 5 & 6 & 7 \\4 & 5 & 6 & 7 & 8 \end{bmatrix}##

##A = \begin{bmatrix}1 & 2 & 3 & 4 & 5 & b_{1} \\2 & 3 & 4 & 5 & 6 & b_{2} \\3 & 4 & 5 & 6 & 7 & b_{3} \\4 & 5 & 6 & 7 & 8 & b_{4} \end{bmatrix} ##

##A = \begin{bmatrix}1 & 0 & -1 & -2 & -3 & -3b_{1}+2b_{2} \\0 & -1 & -2 & -3 & -4 & -2b_{1}+b_{2} \\0 & 0 & 0 & 0 & 0 & b_{1}-2b_{2}+b_{3} \\0 & 0 & 0 & 0 & 0 & 2b_{1}-3b_{2}+b_{4} \end{bmatrix}##

Where do I go from there?

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