how to make nxn matrix

I want to make nxn matrix by follweing rule

n=input

first and last is 1

how can do it?

This is the original formula.

clc;
n=input

A=(n ; n)???

[Walter Roberson]

Sorry, that image is too faint to read.

[WonJong We]

Thank you for the information.

I will change!!

Answer 1

[Walter Roberson]

n = 7

n = 7

d = ones(1,n-2)/2;
M = zeros(n,n) + diag([0,d],+1) + diag([d,0],-1);
M(1) = 1; M(end) = 1;

M

M = 7×7

1.0000 0 0 0 0 0 0 0.5000 0 0.5000 0 0 0 0 0 0.5000 0 0.5000 0 0 0 0 0 0.5000 0 0.5000 0 0 0 0 0 0.5000 0 0.5000 0 0 0 0 0 0.5000 0 0.5000 0 0 0 0 0 0 1.0000

[WonJong We]

Thank you so much!!

[WonJong We]

and... how to make T_0:T_n matrix??

I tried

syms T
B=(T(0):T(n))
A=B(:)

but error

[Walter Roberson]

n = 5

n = 5

syms T0
syms T [n 1]
T = [T0; T]

T = 

[WonJong We]

Thank you so much!!

[WonJong We]

n=5
syms T0
syms T [n 1]
T = [T0 ; T]

error (Invalid variable name.)

hum...

[Walter Roberson]

T = [sym('T0') ; sym('T',[n 1]) ]

[WonJong We]

Thank you very much!!!

clear all; clc; close all;

n=3;
%n=input ('put your n=')

d = ones(1,n-1)/2;
M = zeros(n+1,n+1) + diag([0,d],+1) + diag([d,0],-1);
M(1) = 1; M(end) = 1;
M


T = [sym('T0') ; sym('T',[n 1]) ]

T0=500;
T(n)=300;


T=M*T

than...

T =
 
          T0
  T0/2 + 150
 T1/2 + T3/2
          T3

The values of T2 and T1 are presented as variables.

How do I get a number?

[Walter Roberson]

n=3;
%n=input ('put your n=')

d = ones(1,n-1)/2;
M = zeros(n+1,n+1) + diag([0,d],+1) + diag([d,0],-1);
M(1) = 1; M(end) = 1;
M

M = 4×4

1.0000 0 0 0 0.5000 0 0.5000 0 0 0.5000 0 0.5000 0 0 0 1.0000

T = [sym('T0') ; sym('T',[n 1]) ]

T = 

Tvals = T;
Tvals(1) = 500;
Tvals(n+1) = 300;   %Tn is at position n+1

MT = subs(M*T, T, Tvals)

MT = 

eqn = MT == T

eqn = 

sol = solve(eqn)

sol = struct with fields:
    T0: [1×1 sym]
    T1: [1×1 sym]
    T2: [1×1 sym]
    T3: [1×1 sym]

sol.T0

ans = 

500

sol.T1

ans = 

sol.T2

ans = 

sol.T3

ans = 

300

[WonJong We]

Thank you!