Understanding Matrix Transformations: Solving a Common Homework Problem

[Gurvir]

Homework Statement

Homework Equations

None

The Attempt at a Solution

Well guys, this is a problem I've been having for the last 2 days and with my midterm tomorrow I have no time to fiddle around with it.

So, I do not understand how (where it says b) how

Im going to use a division symbol ( / ) for indicating a break in the line.

(3x+5y)[1 / -2] + (4x+7y)[-1 / 1] is equal to [-x-2y / -2x-3y]

I have no understanding of this, because if you think of [x / y] which means it should be [(3(1) + 5(-2)) / (4(-1) + 7(1))]

which is equal to [3x-10y / -4x+7y] which is not equal what the answer is.

I hope you understand what I am asking and need a response asap, thanks in advance!

 

[Mark44]

Homework Statement

Homework Equations

None

The Attempt at a Solution

Well guys, this is a problem I've been having for the last 2 days and with my midterm tomorrow I have no time to fiddle around with it.

So, I do not understand how (where it says b) how

Im going to use a division symbol ( / ) for indicating a break in the line.

(3x+5y)[1 / -2] + (4x+7y)[-1 / 1] is equal to [-x-2y / -2x-3y]

I have no understanding of this, because if you think of [x / y] which means it should be [(3(1) + 5(-2)) / (4(-1) + 7(1))]

No. It means that (3x + 5y) is a scalar that multiplies each component of the vector <1, -2>^T. Here T means transpose. I'm writing a column vector as a row vector. So you get the vector <3x + 5y, -6x - 10y>^T

Same with (4x + 7y). It multiplies each component of <-1, 1>^T.

Now add the two vectors together and you should get <-x - 2y, -2x - 3y>^T.

which is equal to [3x-10y / -4x+7y] which is not equal what the answer is.

I hope you understand what I am asking and need a response asap, thanks in advance!

 

[Gurvir]

No. It means that (3x + 5y) is a scalar that multiplies each component of the vector <1, -2>^T. Here T means transpose. I'm writing a column vector as a row vector. So you get the vector <3x + 5y, -6x - 10y>^T

Same with (4x + 7y). It multiplies each component of <-1, 1>^T.

Now add the two vectors together and you should get <-x - 2y, -2x - 3y>^T.

AHHH! Hahaha, I'm stressing to much! Thank you so much! Finally, finished Matrix Transformations. Well studying it :D