Matrix rotations

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Rano1234

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Hi so I've been doing matrices recently to revise for an exam, I'm stuck on 2a and have no clue how to approach it, the question is This any help is appreciated Thanks.
 
Rano1234 said:
Hi so I've been doing matrices recently to revise for an exam, I'm stuck on 2a and have no clue how to approach it, the question is This any help is appreciated Thanks.
Click to expand...
Where is... what is 2a.

In addition:

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Please share your work/thoughts about this assignment
 
Matrices.pnghere is the worksheet, i don't really have much working out as im not sure how to attempt it
 
The rule simply states how a matrice is plotted onto a graph however it isnt needed for question 2a
 
Rano1234 said:
The rule simply states how a matrice is plotted onto a graph however it isnt needed for question 2a
Click to expand...
Please STATE the "rule" discussed in your class (that these problems are referring to).
 
I have a question about 1a.
I understand if we want to know what A does to a vector X, then we compute AX
But if what is being asked is what does A do to a matrix B (assume sizes are ok) do we compute AB or BA?
Or am I right that this needs to be given (and probably was in lecture class)?
 
Rano1234 said:
View attachment 15333here is the worksheet, i don't really have much working out as im not sure how to attempt it
Click to expand...
The standard rotation matrix \(\displaystyle \mathscr{R}(\alpha)=\left( {\begin{array}{*{20}{c}} {\cos (\alpha )}&{\sin (\alpha )} \\ { - \sin (\alpha )}&{\cos (\alpha )} \end{array}} \right)\) is a rotation counter clockwise about the origin\(\displaystyle .\)

To get a clockwise rotation use \(\displaystyle \mathscr{R}(-\alpha)=\left( {\begin{array}{*{20}{c}} {\cos (\alpha )}&{-\sin (\alpha )} \\ { \sin (\alpha )}&{\cos (\alpha )} \end{array}} \right)\) note the LaTeX encoding is messed up.

 
Rano1234 said:
The rule simply states how a matrice is plotted onto a graph however it isnt needed for question 2a
Click to expand...
Does the rule tell you the connection between the entries in [MATH]A[/MATH] and what [MATH]A[/MATH] transforms the matrices [MATH]\begin{bmatrix} 1 \\ 0 \end{bmatrix}[/MATH] and [MATH]\begin{bmatrix} 0 \\ 1 \end{bmatrix}[/MATH] to? Do you know these rules? They apply to your problem.
 
So can you tell what that did geometrically to the basis vectors? Scale? Rotation? Shear? Reflection?
 
Too late to edit the above post, but also what does the transformation do to [MATH]\begin{bmatrix} x \\ y \end{bmatrix}[/MATH]? What does that tell you geometrically?
 
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