matrices and linear transformations notes

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Ch 6&7 Core Pure

Math

A-Level Further and Additional Maths

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13 Terms

1
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<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the y-axis , invariant line of x=0

2
New cards
<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the x-axis, invariant line of y=0

3
New cards
<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the line y=x, invariant line of y=x

4
New cards
<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in y=-x, invariant line of y=-x

5
New cards
<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

a rotation angle θ anticlockwise about the origin, invariant point (0,0)

6
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<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line? what does it represent when a=b?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line? what does it represent when a=b?

stretch of scale factor a parallel to the x-axis, and scale factor b parallel to the y-axis (where a=b it is an enlargement scale factor a)

7
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<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the plane x=0

8
New cards
<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the plane y=0

9
New cards
<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the plane z=0

10
New cards
<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

a rotation , angle θ, anticlockwise around the x-axis

11
New cards
<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

a rotation , angle θ, anticlockwise around the y-axis

12
New cards
<p>what does this matrix represent &amp; what are its invariant points/ is there an invariant line?</p>

what does this matrix represent & what are its invariant points/ is there an invariant line?

a rotation , angle θ, anticlockwise around the z-axis

13
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what does the transformation A-1 describe?

the reverse of the transformation represented by matrix A