N = 6; %Set number of subintervals
h = 1/N; %Length of subintervals
diag( ones(N,1))

ans =

     1     0     0     0     0     0
     0     1     0     0     0     0
     0     0     1     0     0     0
     0     0     0     1     0     0
     0     0     0     0     1     0
     0     0     0     0     0     1

N*(diag( 2*ones(N,1))  -diag( ones(N-1,1)),1 )-diag( ones(N-1,1)),-1 )) 
 N*(diag( 2*ones(N,1))  -diag( ones(N-1,1)),1 )-diag( ones(N-1,1)),-1 )) 
                                           
{Error: Invalid expression. When calling a function or
indexing a variable, use parentheses. Otherwise, check for
mismatched delimiters.
} 
N*(diag( 2*ones(N,1))  -diag( ones(N-1,1),1 )-diag( ones(N-1,1),-1 ))

ans =

    12    -6     0     0     0     0
    -6    12    -6     0     0     0
     0    -6    12    -6     0     0
     0     0    -6    12    -6     0
     0     0     0    -6    12    -6
     0     0     0     0    -6    12

K=N*(diag( 2*ones(N,1))  -diag( ones(N-1,1),1 )-diag( ones(N-1,1),-1 ))

K =

    12    -6     0     0     0     0
    -6    12    -6     0     0     0
     0    -6    12    -6     0     0
     0     0    -6    12    -6     0
     0     0     0    -6    12    -6
     0     0     0     0    -6    12

spy(K)
[Warning: MATLAB has disabled some advanced graphics
rendering features by switching to software OpenGL. For
more information, click <a href="matlab:opengl('problems')">here</a>.] 
spy
det(K)

ans =

   3.2659e+05

cond(K)

ans =

   19.1957

b=h*ones(N-1,1)

b =

    0.1667
    0.1667
    0.1667
    0.1667
    0.1667

uh==K\b
{Undefined function or variable 'uh'.
} 
uh=K\b
{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('mldivide')" style="font-weight:bold"> \ </a>
Matrix dimensions must agree.
} 
uh=K/b
{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('mrdivide')" style="font-weight:bold"> / </a>
Matrix dimensions must agree.
} 
size(K)

ans =

     6     6

size(b)

ans =

     5     1

K=N*(diag( 2*ones(N-1,1))  -diag( ones(N-2,1),1 )-diag( ones(N-2,1),-1 ))

K =

    12    -6     0     0     0
    -6    12    -6     0     0
     0    -6    12    -6     0
     0     0    -6    12    -6
     0     0     0    -6    12

uh=K\b

uh =

    0.0694
    0.1111
    0.1250
    0.1111
    0.0694

1:10

ans =

  Columns 1 through 9

     1     2     3     4     5     6     7     8     9

  Column 10

    10

1:2:10

ans =

     1     3     5     7     9

x = h:h:1-h; %A vector containing the node positions except 0 and 1
x

x =

    0.1667    0.3333    0.5000    0.6667    0.8333

exp( [0,1])

ans =

    1.0000    2.7183

exp( [0,2].^2)

ans =

    1.0000   54.5982

exp( [0,2]^2)
{Incorrect dimensions for raising a matrix to a power. Check
that the matrix is square and the power is a scalar. To
perform elementwise matrix powers, use '.^'.
} 
b = h*exp(x.^2);
b

b =

    0.1714    0.1863    0.2140    0.2599    0.3338

b'

ans =

    0.1714
    0.1863
    0.2140
    0.2599
    0.3338

K\b'

ans =

    0.0860
    0.1435
    0.1700
    0.1607
    0.1082

uh=K\b'

uh =

    0.0860
    0.1435
    0.1700
    0.1607
    0.1082

plot(uh)
plot([0;uh;0])
plot(x,uh)