please can someone give me a method to find out for example when they say... 'find the 2x2 matrix that represents this transformation'? is there a method??? if not can someone attach some sort of file with the matrices that i can learn off by heart for the exam;/?
-
We need your support!
We are currently struggling to cover the operational costs of Xtremepapers, as a result we might have to shut this website down. Please donate if we have helped you and help make a difference in other students' lives!
Click here to Donate Now (View Announcement)
MATHS!!! MATRICES
- Thread starter cupcake76
- Start date
Well You See, You Have Two Make Two Pairs Of Simultaneous Equations, And Then Solve Them
First, Note THis Forumula
Object Matrix x Transformation Matrix = Image Matrix
Now, We Need To Find The Transformation Matrice. So, First You Need THe Object Matrice, This is The Matrice Of The Object That is Been Transformed, as in, the original matrice. Take down each X and Y co ordinates of each point, for example, a triangle with 3 edges, the forumla will be like this
x x x
y y y
Where X is the X co ordinate, and y is the y co ordinate.
Now, for the transformation matrix, make it like this
a b
c d
Because thats what we need to find, and the image matrice.... Just like the object matrice, but of the Image co ordinates
So it should look like this
x x x x a b = x x x
y y y c d y y y
Now Make Two Sets of Sumlatenous Equations.
THat Would Be, the First Column x The First Row = Number located in First Column First Row
Then Second Column x The First Row = Number Located in Second Colum First Row
This will be the first Set (which ocntains A And B, Solve It To Find A And B)
Now Do the
First Column x Second Row
And
Second COlumn X Second Row
And then find C and D
Then Substitute
Enjoy =)
First, Note THis Forumula
Object Matrix x Transformation Matrix = Image Matrix
Now, We Need To Find The Transformation Matrice. So, First You Need THe Object Matrice, This is The Matrice Of The Object That is Been Transformed, as in, the original matrice. Take down each X and Y co ordinates of each point, for example, a triangle with 3 edges, the forumla will be like this
x x x
y y y
Where X is the X co ordinate, and y is the y co ordinate.
Now, for the transformation matrix, make it like this
a b
c d
Because thats what we need to find, and the image matrice.... Just like the object matrice, but of the Image co ordinates
So it should look like this
x x x x a b = x x x
y y y c d y y y
Now Make Two Sets of Sumlatenous Equations.
THat Would Be, the First Column x The First Row = Number located in First Column First Row
Then Second Column x The First Row = Number Located in Second Colum First Row
This will be the first Set (which ocntains A And B, Solve It To Find A And B)
Now Do the
First Column x Second Row
And
Second COlumn X Second Row
And then find C and D
Then Substitute
Enjoy =)
hmm , i dont quite understand anything past
So it should look like this
x x x x a b = x x x
y y y c d y y y
Now Make Two Sets of Sumlatenous Equations.
THat Would Be, the First Column x The First Row = Number located in First Column First Row
Then Second Column x The First Row = Number Located in Second Colum First Row
This will be the first Set (which ocntains A And B, Solve It To Find A And B)
Now Do the
First Column x Second Row
And
Second COlumn X Second Row
And then find C and D
Then Substitute
/quote]
Can u please perhaps upload pics of working out step by step , and number what your saying accordingly , it would make it much easier , as my weakness lies within Matrices...
thanks in advance.