How do I show a quiver plot from a matrix?

I am trying to graph this direction field:

x' = (1 1; 4 1)x

This is my code:

a = [1 1;4 1];
x = [x y];
[x,y] = meshgrid(-10:1:10,-10:1:10);
dx = 1;
dy = a.*x.*1;
r = ( dx.^2 + dy.^2 ).^0.5;
u = dx./r;
v = dy./r;
figure
quiver(x,y,u,v);

It returns this error:

ꕋerror: QuiverPlot: product: nonconformant arguments (op1 is 2x2, op2 is 21x21)

error: called from

QuiverPlot at line 5 column 4

I guess my x vector does not have the same dimension as my a vector, even though a has two columns and x has two rows.

As a side note, this problem was given by Boyce and Diprima's textbook with no context regarding the code.

[Dylan Voss]

I edited my code, putting a semicolon in matrix t (formerly matrix x):

a = [1 1;4 1];
[x,y] = meshgrid(-10:1:10,-10:1:10);
t = [x;y];
dx = 1;
dy = a.*t.*1;
r = ( dx.^2 + dy.^2 ).^0.5;
u = dx./r;
v = dy./r;
figure
quiver(x,y,u,v);

Matrix x is still a 42 by 21 matrix evidently.......??

Answer 1

[Cris LaPierre]

The issue is with your calculation of dy. Variable a is 2x2, but t is 42x21.

[Dylan Voss]

Why is t 42 by 21?

[Cris LaPierre]

Because you create it using x and y, specifically placing y directly underneath x, and they are each 21x21. Perhaps take a look at the documentation for meshgrid.