1. Order of a matrix Number of rows by number of columns 2. Square matrix Matrix of order NxN 3. Leading diagonal Diagonal of matrix from top left to bottom right 4. Conditions for two matrices to be equal - must have same order - each element in one matrix must be equal to the correspondi...
1 order of a matrix number of rows by number of columns 2 square matrix matrix of order nxn 3 leading diagonal diagonal of matrix from top left to bottom right 4 conditions for two matrices
Edexcel A-Level Mathematics - Core Pure Maths
Study online at https://quizlet.com/_8kjdlu
1. Order of a matrix Number of rows by
number of columns
2. Square matrix Matrix of order NxN
3. Leading diagonal Diagonal of matrix from top
left to bottom right
4. Conditions for two matrices to - must have same order
be equal - each element in one matrix
must be equal to the
corresponding ele- ment in
the other
5. Matrices which you can't add are... non-conformable for addition
6. Matrices which you can't non-conformable for
multiply are... multiplication
8. What does it mean for matrix multi- AB=BA
plication A and B if each matrix
only affects one of the unit vectors?
9. Geometrically what happens Returns object to original
when multiply by I? position
10. How do transformations explain
asso- ciativity of matrix In matrix (AB)C, AB
multiplication?
represents transformation of
B followed by A. (AB)C
represents transformation of
C followed by AB so (AB)C
rep- resents C followed by B
followed by A
In matrix A(BC), BC
represents transformation of
1/
, Edexcel A-Level Mathematics - Core Pure Maths
Study online at https://quizlet.com/_8kjdlu
C followed by B and A(BC) represents
transforma- tion of (BC) followed by
A so A(BC) represents C followed by
B fol- lowed by A
2/
, Edexcel A-Level Mathematics - Core Pure Maths
Study online at https://quizlet.com/_8kjdlu
11. Explain why can't you represent The origin is invariant under
trans- lations with 2x2 matrix? all linear transformations
(transforma- tions that can be
represented by
a 2x2) matrix. A translation
would require the origin to
not map onto itself
12. In 3D transformations how do you
de- scribe rotations? You take anticlockwise and
clock- wise about an axis by
looking from the positive end
of the axis towards the origin
13. Things to mention when describing a
sheer? - which line is fixed e.g x axis
- an example of a point and
its im- age that's not on the
14. Matrices for a shear with x and y
axis fixed respectively fixed line
15. How to find shear factor geometrical- Shear with x axis fixed ((1,k),
ly? (0,1)) Shear with y axis fixed
((1,0),(k,1))
Work out distance from a
point P and its image using
Pythagoras P' and call it d1.
Work out distance from that
point P to invariant line and
call it d2. Do this by finding
equation of invari- ant line
and finding equation of line
perpendicular to the invariant
16. How to find invariant line of shear line that passes through P
fac- tor geometrically? and finding where these lines
cross and using Pythagoras'.
The shear factor is d1/d2.
Join point A and B and extend
the line.
3/
, Edexcel A-Level Mathematics - Core Pure Maths
Study online at https://quizlet.com/_8kjdlu
Do same for the images A' and B' so
that the two lines cross.
Repeat this for another two points
and join the points of intersection.
This line is the invariant line.
4/
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