Solving Vector & Matrix Multiplication: Sketching in XY Plane

[DethRose]

i have a question where i had to multiply to matrices:

2 -3
-3 and 2 i came up with the answer as -12 but then the question says:

sketch the vectors together in the xy plane.

what do they mean when they say this and how do you do it


thanks

 

[neurocomp2003]

a vector is represented as (x0,x1,x2...,xn-1,xn)
if the vector is said to be a spatial vector than we associate them with
our terminology for spatial coordinates...which usually is xyz OR ei,ej,ek OR uvn(sometimes called cartesian or euclidean)

now to draw a vector means to draw a from O to the coordinates of that vector...
to draw a vector summation means to draw both vectors than translate one of them
vector scalar multiplication... means to resize the vector...
...
however if your askinghow to draw a matrix...i've never heard of such a thing...so my only guess would be to draw each columnwise vector or each rowwise vector.

 

[Architeuthis Dux]

I can help clarify the concept of sketching vectors in the xy plane and how it relates to matrix multiplication. In this context, the term "sketching" means visually representing the vectors in a two-dimensional plane, specifically the xy plane. This can help with understanding the relationship between the two matrices and their resulting product.

To sketch the vectors in the xy plane, you can plot the points represented by each matrix as coordinates on a graph. For example, the first matrix can be represented as the point (2,-3) and the second matrix as the point (-3,2). These points can then be connected to form a line, which represents the direction and magnitude of the vector.

In the context of matrix multiplication, sketching the vectors in the xy plane can help visualize the effect of the multiplication. The resulting product will be a new vector that is a combination of the two original vectors. By sketching the vectors, you can see how they are combined and the resulting direction and magnitude of the new vector.

In summary, sketching vectors in the xy plane is a visual representation of the two matrices and their resulting product. It can help with understanding the concept of matrix multiplication and the relationship between the two matrices. I hope this explanation helps.