Linear Transformations

The vectors w1 = (7; 8), w2 = (8; 9) form an (ordered) basis, B, for R^2. Define a real linear transformation, (T) : R^2:R^2
by ((x; y)) = (5x 9y; 9x + 11y). Working from its denition, determine

M_B^B

(T), the matrix of T with respect to the ordered basis B.

To be perfectly honest I haven't the slightest idea how to approach this. Any help would be greatly appreciated.

Reply 1

Happy2Guys1Hammer

Anybody, Please help!

Reply 2

DPLSK

Happy2Guys1Hammer

The vectors

w_1=(7, 8), w_2 = (8, 9)

form an (ordered) basis,

\mathcal{B}

, for

\mathbb{R}^2

.

Define a real linear transformation,

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

(x, y)=(5x + 9y, 9x + 11y)

.

Determine

M_{\mathcal{B}}(T)

, the matrix of

T

with respect to the ordered basis

\mathcal{B}

Well you first need to write down the transformation matrix which sends

(x, y)

(5x + 9y, 9x + 11y)

.

Consider

Unparseable latex formula:

\begin{pmatrix}[br] a & b\\[br] c & d[br]\end{pmatrix}\begin{pmatrix}[br] x\\[br] y\end{pmatrix}=\begin{pmatrix}[br] 5x + 9y\\[br] 9x + 11y\end{pmatrix}

where

a, b, c, d

are constants to be determined.

After this you'll probably need to use a change of basis formula or something along those lines. Click here for something which might help.

I hope this helps.

Darren

(edited 12 years ago)