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Matrix Transformation

A transformation in the plane is represented by a 2 x 2 matrix.
Under this transformation, the point (-3,-8) is transformed to (7,7) and the point (3,-2) is transformed to (-1,-4).

(i) What is the matrix representing this transformation?

(ii) Find coordinates of the image of the point (3,0) under this transformation

Reply 1

Dirac Spinor

write down what you know:
let

\mathbf{M}=\begin{pmatrix} a & b \\ c & d \end{pmatrix}

be the unknown transformation.
it follows that:

\begin{pmatrix} a & b \\ c & d \end{pmatrix}\begin{pmatrix} -3 & 3 \\ -8 & -2 \end{pmatrix}= \begin{pmatrix} 7 & -1 \\ 7 & -4 \end{pmatrix}

.
If you know how to multiply matrices then it should be easy to turn the LHS into one matrix. You can then equate the entries and solve simultaneous equations. There may be a more elegant way but the simultaneous equations are quite handily laid out.

Reply 2

kaosu_souzousha

Ben-smith gives a good explanation for part (i)

for part (ii) you just multiply your obtained transformation matrix by point (3 , 0 ) and get an image

Reply 3

Dirac Spinor

Original post by kaosu_souzousha

Ben-smith gives a good explanation for part (i)

for part (ii) you just multiply your obtained transformation matrix by point (3 , 0 ) and get an image